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NATURAL PHILOSOPHY & ASTRONOMY, 

BY DENISON OLMSTED, 

Professor of Natural Philosophy and Astronomy, in Yale College. 

PUBLISHED BY COLLINS, BROTHER AND CO. 

NEW-YORK. 

1^ -/ 

OLMSTED'S SCHOOL ASTRONOMY. 

This work having been used as a class book in a number 
of the celebrated schools of Philadelphia, the publishers have 
been favoured with strong testimonials of their approbation, 
among which are the following : — 

From the Rev. Charles Henry Alden, Principal of the 
Philadelphia High School for Young Ladies. 

I have examined with great care " Olmsted's Compeu' 
dium of Astronomy," and have taken a highly intelligent 
class in my institution critically through it. We have long 
felt the want of a Text Book in this most interesting science, 
and the author of this merits the thanks of the profession for 
a Treatise so entirely methodical and lucid, and so admirably 
adapted to our more advanced classes. Judging of its merits 
by the interest evinced by my pupils, as well as from its in- 
trinsic excellence, I cannot too strongly recommend its gene- 
ral adoption. 



From Samuel Jones, A, M., Principal of the Classical and 
Mathematical Institute, South Seventh St., Phil. 
I am using " Olmsted's Compendium of Astronomy" in my 
school, and fully concur with the Rev. Mr. Alden in his opin- 
ion of the work. 



From Charles Deocter Cleveland, A. M., late Professor 
in Dickinson College, Carlisle, Pa. 
Gentlemen, 
I have not vanity enough, I assure you, to suppose for a 
moment that any thing I can say will add to the fame of Pro- 



fessor Olmsted's Works on Natural Philosophy; but as yoa 
ask me my opinion of his " Compendium of Astronomy," I 
will say, that I intend to introduce it into my school, consider- 
ing it the best work of the kind with which I am acquainted. 

From Richard W. Green, A* M., Principal of the English 
Department of the Academy of the University of Pa., Avihor 
of an Arithmetical Guide, Inductive Algebra^ tSfC. 

I have read through Professor Olmsted's " Compendium of 
Astronomy ;" I am much pleased with the explanations and 
illustrations employed by the author, and I can testify from 
my own experience, that the work is well calculated to revive 
in a forcible manner, any Astronomical knowledge obtained in 
scholastic days. I commend the book as well adapted to the 
purpose of instruction of the noble science of which it treats. 

This work has also been very favorably noticed in various 
periodicals. The following discriminating remarks from the 
New Haven Record, are understood to be from the pen of an 
able and experienced teacher of Astronomy, 

Olmsted's School Astronomy. — It is with peculiar plea- 
sure we notice the appearance of this work, small in size, but 
containing more matter than many larger books. There is 
probably no instructor of much experience who has not felt 
serious inconvenience from the want of a proper text-book in 
this department of science, as taught in our academies and 
higher schools. The treatise before us, however, is one 
which, after a careful perusal and the use of it as a text-book, 
we can most cheerfully recommend as eminently adapted to 
supply the vacancy heretofore existing. Our author is par- 
ticularly happy in the arrangement and division of the various 
subjects discussed ; each occupying its appropiate place, in- 
volving no principle which has not been previously considered. 
He aims to fix in the mind the great principles of the science, 
first by stating them in the most concise and perspicuous 
terms, and then by lucid and familiar illustrations, without 
entering into an indiscriminate and detailed statement of a 
multiplicity of statistics, which only burden the memory and 
discourage the student. 

The learner is early made acquainted with the use of the 
globes, which greatly assists him in understanding the causes 



3 

of various phenomena which otherwise would be wholly un- 
intelligible. The student in his progress finds himself in 
possession of the keys of knowledge, and is highly pleased 
and encouraged in being able to anticipate effects and assign 
their true causes, which before seemed a mystery. Indeed, 
we feel assured, that this compendium need only be known to 
competent and judicious instructors, in order to secure its 
cheerful introduction into our schools and academies as an 
important auxiliary to science. Those who have had the 
misfortune to toil for many a tedious hour in treasuring up 
insulated facts in this science, without a knowledge of the 
principles upon which they depend, and consequently without 
any knowledge of the subject, will be fully convinced, after a 
patient perusal of the work under consideration, that the study 
of Astronomy is not necessarily dry and uninteresting, but 
that the difficulty arises in a great measure from an erroneous 
method of studying the subject. A. 

OLMSTED'S SCHOOL PHILOSOPHY: 

Or a Compendium of Natural Philosophy, adapted to the 
y^e of the general reader^ and to Schools and Academies, 

The following Recommendations, obligingly communicat- 
ed, without solicitation, to the author, attest the estimation 
in which the work is held by the most eminent judges. 
From the Hon. Simeon De Witt, late Surveyor General of the 
State of New York, and Chancellor of the University » 

Professor D. Olmsted. 

Dear Sir, — ^I some time ago received your Compendium 
of Natural Philosophy, for which I take this opportunity of 
making my thankful acknowledgments. I consider it as 
one of the best treatises of the kind for the instruction of 
those who have not had a mathematical education, and as an 
excellent Text Book for those who study Natural Philosophy 
with the help of mathematical demonstrations. 

Albany, Jan. 27, 1834. 



From Professor E. A, Andrews, of Boston, 
" I am glad that you are about to give your Compendium 
in a cheaper form, for the use of schools. There is no work 
that I have seen, that compares with it, for common use ; 



and I have no doubt that when, in consequence of its altered 
form and price, it shall be better adapted to the views of those 
who conduct such institutions, it will acquire that general 
popularity which it so well deserves," 



From the Rev. S. Center, of the Albany High School, 

" I have introduced the Compendium into my school, and 
caused it to be introduced into two others. I assure you 
that it meets with a welcome reception from those who have 
examined it. We like the work for its practical character. 
Its illustrations are happy, its facts numerous, and its explan- 
ations of common phenomena, are to a great extent new and 
interesting. The arithmetical problems which accompany 
the statements and illustrations, are, in my opinion, a valua- 
ble feature in the work." 



INTRODUCTION TO ASTRONOMY, one volume, 8vo. 
For the use of Colleges. Second Edition. 

Nearly all who have written treatises on Astronomy de- 
signed for teachers, appear to have erred in one of two ways ; 
they have either disregarded demonstrative evidence and re- 
lied on mere popular illustrations, or they have exhibited the 
elements of the science in naked mathematical formulae. The 
former are usually diffuse and superficial ; the latter techni- 
cal and abstruse. 

In the above work the author has fully succeeded in unit- 
ing the advantages of both methods. He has, firstly, estab- 
lished the great principles of Astronomy on a mathematical 
basis ; and, secondly, rendered the study interesting and intel- 
ligible to the learner by easy and familiar illustrations. 

OLMSTED'S INTRODUCTION TO NATURAL PHI- 
LOSOPHY, one volume, 8vo. Designed as a Text-Book 
for Colleges. Fifth Edition. 
The rapidity with which this work has been sold and 

introduced into the various Colleges and Academies in the 

United States, is sufficient evidence of the estimation in which 

it is held. 



COMPENDIUM OF ASTRONOMY; 

CONTAINING THE 

ELEMENTS OF THE SCIENCE, 

FAMILIARLY EXPLAINED AND ILLOSTRATED, 

WITH THE LATEST DISCOVERIES. 

ADAPTED TO THE USE OF 

SCHOOLS AND ACADEMIES, 

AND OF THE 

GENERAL READER. 

SIXTH EDITION. 

BY DENISON OLMSTED, A. M. 

PROFESSOR OF Natural philosophy and astronomy in yale college. 



NEW. YORK : 

PUBLISHED BY COLLINS, BROTHER & CO., 

254 pearl-street. 

1844. 



Q±)H^ 



Entered according to Act of Congress, in the year 1839, by 

DENISON OLMSTED, 

in the Clerk's office, of the District Court of Connecticut. 



GCft 

Judge and Mrs. f.R.HItt 
Dec. 11, 1936 



PREFACE. 



This small volume is intended to afford to the General 
Reader, and to the more advanced pupils of our Schools and 
Academies, a comprehensive outline of Astronomy with its 
latest discoveries. For its perusal, no further acquaintance 
with mathematics is necessary, than a knowledge of common 
arithmetic ; although some slight knowledge, at least, of ge- 
ometry and trigonometry will prove very useful. 

By omitting mathematical formulae, and employing much 
familiar illustration, we have endeavored to bring the leading 
facts and doctrines of this noble and interesting science, 
within the comprehension of every attentive and intelligent 
reader. In no science, more than in this, are greater advan- 
tages to be derived from a lucid arrangement — an order which 
brings out every fact and doctrine of the science, just in the 
place where the mind is ready to receive it. A certain matu- 
rity of mind, and power of reflection, are, however, indispen- 
sable for understanding this science. Astronomy is no study 
for children. Let them be employed on subjects more suited 
to the state of their capacities, until those faculties are more 
fully developed, which will enable them to learn to conceive 
correctly of the celestial motions. A work on Astronomy 
that is very easy, must be very superficial, and will be found 
to enter little into the arcana of the science. The riches 
of this mine lie deep ; and no one can acquire them, who 
is either incompetent or unwilling to penetrate beneath the 
surface. 



Although this treatise is based on the larger work of the 
author, (" Introduction to Astronomy,") prepared for the stu- 
dents of Yale College, yet it is not merely an abridgement of 
that. It contains much original matter adapted to the peculiar 
exigencies of the class of readers for whom it is intended. 
The few passages taken verbatim from astronomical writers, 
are not, as in the larger work, always accredited to their res- 
pective authors, as this was deemed unimportant in a work of 
this description. 

It is strongly recommended to all who study this science, 
even in its most elementary form, early to commence learning 
the names of the constellations, and of the largest of the in- 
dividual stars, in the order in which they are described in the 
last part of the work. A celestial globe will be found a 
most useful auxiliary in this as in every other part of As- 
tronomy. If it cannot supersede, it may greatly aid reflection. 
The reader also should, if in his power, take frequent oppor- 
tunities of viewing the heavenly bodies through the telescope. 
This will add much to his intelligence, and increase his inter- 
est in the study. 



CONTENTS. 



Preliminary Observations, - - - Page 1 

Part I. OF THE EARTH. 

Chapter I. — Of the Figure and Dimensions of the Earth, 

and the Doctrine of the Sphere, - - - 5 

Chapter II. — Of the Diurnal Revolution — Artificial 

Globes, 21 

Chapter III.— Of Parallax, Refraction, and Twilight, 36 

Chapter IV.~Of Time, 45 

Chapter V. — Of Astronomical Instruments — Figure 

and Density of the Earth, - - - - 51 

Part 11. OF THE SOLAR SYSTEM. 

Chapter I. — Of the Sun — Solar Spots — Zodiacal Light, 70 
Chapter II. Of the Apparent Annual Motion of the 

Sun — Seasons — Figure of the Earth's Orbit, - 79 
Chapter III. — Of Universal Gravitation — Kepler's 

Laws, — Motion in an Elliptical Orbit — Precession 

of the Equinoxes, - - - - - -91 

Chapter IV. — Of the Moon — Phases, Revolutions, - 110 

Chapter V.— Of Eclipses, 137 

Chapter VI.— Of Longitude— Tides, - - - 150 

Chapter VII.— Of the Planets— the Inferior Planets, 

Mercury and Venus, - - - - - 1 67 

Chapter VIII. — Of the Superior Planets — Mars, Jupiter, 

Saturn and Uranus — Ceres, Pallas, Juno and Vesta, 1 83 



VI CONTENTS. 

Page 

Chapter IX. — Of the Motions of the Planetary System 
— Quantity of Matter in the Sun and Planets — 
Stability of the Solar System, - - - - 205 

Chapter X.— Of Comets, 218 

Part III. OF THE FIXED STARS AND THE SYS- 
TEM OF THE WORLD. 

Chapter I. — Of the Fixed Stars Constellations, - 235 

Chapter II. — Of Clusters of Stars — Nebulae — Variable 

Stars — Temporary Stars — Double Stars, - - 247 

Chapter III. — Of the Motions of the Fixed Stars — Dis- 
tances — Nature, 255 

Chapter IV.— Of the System of the World, - - 265 



COMPENDIUM OF ASTRONOMY. 



PRELI3IINARY OBSERVATIONS. 

1. Astronomy is that science which treats of the heav- 
enly bodies. 

More particularly, its object is to teach what is known 
respecting the Sun, Moon, Planets, Comets, and Fixed 
Stars ; and also to explain the methods by which this 
knowledge is acquired. 

Astronomy is sometimes divided into Descriptive, 
Physical, and Practical. Descriptive Astronomy re- 
spects foc^5 ; Physical Astronomy, causes ; Practical As- 
tronomy, the means of investigating the facts, whether 
by instruments, or by calculation. It is the province of 
Descriptive Astronomy to observe, classify, and record, 
all the phenomena of the heavenly bodies, whether per- 
taining to those bodies individually, or resulting from 
their motions and mutual relations. It is the part of 
Physical Astronomy to explain the causes of these phe- 
nomena by investigating and applying the general laws 
on which they depend ; especially by tracing out all the 
consequences of the law of universal gravitation. Prac- 
tical Astronomy lends its aid to both the other depart- 
ments. 

2. Astronomy is the most ancient of all the sciences. 
At a period of very high antiquity, it was cultivated in 
Egypt, in'Chaldea, and in India. Such know^ledge of 
the heavenly bodies as could be acquired by close and 
lon^ continued observation, without the aid of instru- 



1 . Define x^stronomy. What does it teach ? Name the three 
parts into which it is divided. What does Descriptive Astron- 
omy respect ? What does Physical Astronomy 1 What does 
Practical Astronomy ? What is the peculiar province of each '*■ 
1 



PRELIMINARY OBSERVATIONS. 



^ merits, was diligently amassed ; and tables of the celes- 
tial motions were constructed, which could be used in 
predicting eclipses, and other astronomical phenomena. 

About 500 years before the Christain era, Pythago- 
ras, of Greece, taught astronomy at the celebrated school 
at Crotona, (a Greek town on the southeastern coast of 
Italy,) and exhibited more correct views of the nature 
of the celestial motions, than were entertained by any 
other astronomer of the ancient world. His views, how- 
ever, were not generally adopted, but lay neglected for 
nearly 2000 years, when they were revived and estab- 
lished by Copernicus and Galileo. The most celebrated 
astronomical school of antiquity, was at Alexandria in 
Egypt, which was established and sustained by the Ptol- 
emies, (Egyptian princes,) 300 years before the Chris- 
tian era. The employment of instruments for measur- 
ing angles, and bringing in trigonometrical calculations 
to aid the naked powers of observation, gave to the Alex- 
andrian astronomers great advantages over all their pre- 
decessors. 

The most able astronomer of the Alexandrian school 
was Hipparchus, who was distinguished above all the 
ancients for the accuracy of his astronomical measure- 
ments and determinations. The knowledge of astron- 
omy possessed by the Alexandrian school, and recorded 
in the Almagest, or great work of Ptolemy, constituted 
the chief of what was known of our science during the 
middle ages, until the fifteenth and sixteenth centuries, 
when the labors of Copernicus of Prussia, Tycho Brake 



2. Trace the history of Astronomy. Among what ancient 
nations was it cultivated ? What kind of knowledge of the 
heavenly bodies was amassed ? Who was Pythagoras? When 
and where did he live ? Where was his school ? How correct 
were his views ? Were they generally adopted ? Give an ac- 
count of the Alexandrian school. When was it established and 
by whom ? What gave it great advantages over all its prede- 
cessors ? Give some account of Hipparchus — of Ptolemy — of 
Copernicus — of Tycho Brahe— of Kepler— of Galileo — of 
Newton — of La Place. Specify the respective labors of each. 



PRELIMINARY OBSERVATIONS. 3 

of Denmark, Kepler of Germany, and Galileo of Italy, 
laid the solid foundations of modern astronomy. Coper- 
nicus expounded the true system of the world, or the 
arrangement and motions of the heavenly bodies ; Ty- 
cho Brahe carried the use of instruments, and the art of 
astronomical observation, to a far higher degree of accu- 
racy than had ever been done before ; Kepler discovered 
the great laws which regulate the movements of the 
planets ; and Galileo, having first enjoyed the aid of the 
telescope, made innumerable discoveries in the solar 
system. Near the beginning of the eighteenth century, 
Sir Isaac Newton discovered, in the law of universal 
gravitation, tho great principle that explains the causes 
of all celestial phenomena ; and recently. La Place has 
more fully completed what Newton begun, having fol- 
lowed out all the consequences of the law of universal 
gravitation, in his great work, the Mecanique Celeste. 

3. Among the ancients, astronomy was studied chiefly 
as subsidiary to astrology. Astrology was the art of di- 
vining future events by the stars. It was of two kinds, 
natural and judicial. Natural Astrology, aimed at pre- 
dicting remarkable occurrences in the natural world, as 
eathquakes, volcanoes, tempests, and pestilential dis- 
eases. Judicial Astrology, aimed at foretelling the fates 
of individuals, or of empires. 

4. Astronomers of every age, have been distinguished 
for their persevering industry, and their great love of ac- 
curacy. They have uniformly aspired to an exactness 
in their inquiries, far beyond what is aimed at in most 
geographical investigations, satisfied with nothing short 
of numerical accuracy wherever this is attainable ; and 
years of toilsome observation, or laborious calculation, 
have been spent with the hope of attaining a few se- 



3. Define x\strology. What was Natural and what Judicial 
Astrology ? 

4. What is said of the industry and accuracy of astrono- 
mers ? Can this science be taught by artificial aids alone ? 



4 PRELIMINARY OBSERVATIONS. 

conds nearer to the truth. Moreover, a severe but de- 
lightful labor is imposed on all, who would arrive at a 
clear and satisfactory knowledge of the subject of astron- 
omy. Diagrams, artificial globes, orreries, and familiar 
comparisons and illustrations, proposed by the author or 
the instructor, may afford essential aid to the learner, 
but nothing can convey to him a perfect comprehension 
of the celestial motions, without much dihgent study 
and reflection. 

5. In this treatise, we shall for the present assume the 
Copernican system as the true system of the world, 
postponing the discussion of the evidence on which it 
rests to a late period, when the learner has been made ex- 
tensively acquainted with astronomical facts. This sys- 
tem maintains (1,) That the «p/7«re7ii diurnal revolution 
of the heavenly bodies, from east to west, is owing to 
the real revolution of the earth on its own axis from 
west to east, in the same time ; and (2.) That the sun 
is the center around which the earth and planets all re- 
volve from west to east, contrary to the opinion that the 
earth is the center of motion of the sun and planets. 



5. What system is assumed as the true system of the world? 
Specify the two leading points in the Copernican system. 



PART I. OF THE EARTH, 



CHAPTER I. 



OF THE FIGURE AND DIMENSIONS OF THE EARTH, AND THE 

DOCTRINE OF THE SPHERE. 

6. The figure of the earth is nearly globular. This 
fact is known, first, by the circular form of its shadow 
cast upon the moon in a lunar eclipse ; secondly, from 
analogy, each of the other planets being seen to be 
spherical ; thirdly, by our seeing the tops of distant ob- 
jects while the other parts are invisible, as the topmast 
of a ship, while either leaving or approaching the shore, 
or the lantern of a light-house, which when first descried 
at a distance at sea, appears to glimmer upon the very 
surface of the water ; fourthly, by the testimony of nav- 
igators v/ho have sailed around it ; and, finally, by ac- 
tual observations and measurements, made for the ex-- 
press purpose of ascertaining the figure of the earth, by 
means of which astronomers are enabled to compute the 
distances from the center of the earth of various places 
on its surface, which distances are found to be nearly 
equal. 

The effect of the rotundity of the earth upon the ap- 
pearance of a ship, when either leaving or approaching 
the spectator, is illustrated by Fig. 1. 

As light proceeds in straight lines, it is evident that, 
if the earth is round, the top of the ship ought to com.e 
into view before the lower parts, when the ship is ap- 
proaching the spectator at A, and to remain longest in 
view when the ship is leaving him. But, were the earth 



6. What is the figure of the earth 1 Enumerate the various 
proofs of its rotundity. 

1* 




a continued plane, then the spectator would see all parts 
of the ship at the same time, as is represented in the an- 
nexed figure. 

Fig. 2. 




7. The foreguihu c*MisiuL:iuLiuns show that the form 
of the earth is spherical ; but more exact determinations 
prove, that the earth, tliough nearly globular, is not ex- 
actly so ; its diameter from the north to the south pole 
is about 26 miles less than through the equator, giving 
to the earth the form of an oblate spheroid, or a flattened 
sphere resembling an orange. We shall reserve the ex- 



FIGURE AND DIMENSIONS. 7 

planations of the methods by which this fact is estab- 
lished, until the learner is better prepared than at present 
to understand them. 

The mean or average diameter of the earth, is 7912.4 
miles, a measure which the learner should fix in his 
memory as a standard of comparison in astronomy, and 
of which he should endeavor to form the most adequate 
conception in his power. The circumference of the 
earth is about 25.000 miles. Although the surface of 
the earth is uneven, sometimes rising in high mountains, 
and sometimes descending in deep valleys, yet these ele- 
vations and depressions are so small in comparison with 
the immense volume of the globe, as hardly to occasion 
any sensible deviation from a surface uniformly curvi- 
hnear. The irregularities of the earth's surface, in this 
view, are no greater than the rough points on the rind 
of an orange, which do not perceptibly interrupt its con- 
tinuity ; for the highest mountain on the globe is only 
about five miles above the general level ; and the deep- 
est mine hitherto opened is only about half a mile.* 

5 i 

Now = , or about one sixteen hundredth part 

7912 1582 ^ 

of the whole diameter, an inequality which, in an arti- 
ficial globe of eighteen inches diameter, amounts to only 
the eighty eighth part of an inch. 

8. The greatest difficulty in the way of acquiring 
correct views in astronomy, arises from the erroneous 
notions that pre-occupy the mind. To divest himself 



7. What is the exact figure of the earth 1 How much greater 
is its diameter through the equator than through the poles ? 
What is the mean average diameter of the earth 1 What is its 
circumference 1 Do the inequalities on the earth's surface af- 
fect its rotundity ? To what may these be compared ? How 
high is the highest mountain above the general level ? How 
deep is the deepest mine ? To how much would this amount 
on an artificial globe eighteen inches in diameter ? 

* Sir John Herschel. 



8 THE EARTH. 

of these, the learner should conceive of the earth as a 
huge globe occupying a small portion of space, and en- 
circled on all sides with the starry sphere. He should 
free his mind from its habitual proneness to consider one 
part of space as naturally up and another down^ and 
view himself as subject to a force which binds him to 
the earth as truly as though he were fastened to it by 
some invisible cords or wires, as the needle attaches it- 
self to all sides of a spherical loadstone. He should 
Fig. 3. 




dwell on this point until it appears to him as truly up in 
the direction of BB, CC, DD, (Fig. 3,) when he is at 
B, C, and D, respectively, as in the direction AA, when 
he is at A. 



DOCTRINE OF THE SPHERE, 



^ 9. The definitions of the different lines, points, and 
circles, which are used in astronomy, and the proposi- 
tions founded upon them, compose the Doctrine of the 
Sphere. 



^ 8. Whence arises the greatest difficulty in acquiring correct 
views in astronomy ? How should the learner conceive of 
the earth ? Illustrate by figure 3. 
9. Doctrine of the sphere — define it. 



DOCTRINE OF THE SPHERE. 



10. A section of a sphere by a plane cutting it in any 
manner, is a circle. Great circles are those which pass 
through the center of the sphere, and divide it into two 
equal hemispheres : Small circles, are such as do not 
pass through the center, but divide the sphere into two 
unequal parts. Every circle, whether great or small, is 
divided into 360 equal parts called degrees. A degree, 
therefore, is not any fixed or definite quantity, but only 
a certain aliquot part of any circle.* 

The axis of a circle, is a straight line passing through 
its center at right angles to its plane. 



* As this work may be read by some who are unacquainted with 
even the rudiments of geometry, we annex a few particulars respecting 
angular measurements. 

A line drawn from the center to the circumference of a circle is 
called a radius, as CD, fig. 4. 

Anv part of the circumference of a circle is called an arc, as AB, 
:BD. 



Fig. 4. 



An angle is measured by the 
arc included between two radii. 
Thus, in the annexed figure, the 
angle contained between tlie two 
radii CA and CB, that is, the an- 
gle ACB, is measured by the arc 
AB. But this arc is the same part 
of the smaller circle that EF is of 
the greater. The arc AB there- 
fore contains the same number of 
degrees as the arc EF, and either 
may be taken for the measure of 
the angle ACB. As the whole 
circle contains 360", it is evident 
that the quarter of a circle, or quad- 
rant ABD, contains 90°, and the 
semicircle ABDG contains 180°. 

The compleviciii of an arc or an- 
gle, is what it wants of 90^. Thus BD is the complement of AB, and 
AB is the complement of BD. If AB denotes a certain number of de- 
grees of latitude, BD will be the complement of the latitude or the co- 
laiitude, as it is commonly written. 

The supplement of an arc or angle, is what it wants of 180°. 
Thus BA is the supplement of GDB, and GDB, is the supplement 
of BA. If BA were 20° of longitude, GDB its supplement would 
be 160°. 

An angle is said to be subtended by the side which is opposite to it. 
Thus in tlie triangle ACK, the angle at C is subtended by the side AK, 
the angle at A by CK, and the angle at K by CA. In like manner a 
side is said to be subtended by an angle, as AK by the angle at C. 




10 THE EARTH. 

The pole of a great circle, is the point on the sphere 
where its axis cuts through the sphere. Every great 
circle has two poles, each of which is every where 90® 
from the great circle. 

All great circles of the sphere cut each other in two 
points diametrically opposite, and consequently, their 
points of section are 180° apart. 

A great circle which passes through the pole of an- 
other great circle, cuts the latter at right angles. 

The great circle which passes through the pole of an- 
other great circle and is at right angles to it, is called a 
secondary to that circle. 

The angle made by two great circles on the surface 
of the sphere, is measured by the arc of another great 
circle, of which the angular point is the pole, being the 
arc of that great circle intercepted between those two 
circles. 

11. In order to fix the position of any plane, either on 
the surface of the earth or in the heavens, both the earth 
and the heavens are conceived to be divided into sepa- 
rate portions by circles, which are imagined to cut 
through them in various w^ays. The earth thus inter- 
sected is called the terrestrial, and the heavens the ce- 
lestial sphere. The learner will remark, that these cir- 
cles have no existence in nature, but are mere land- 
marks, artificially contrived for convenience of refer- 



10. What figure is produced by the section of a sphere? 
Dejfine great circles. Define small circles. Into how many 
degrees is every circle divided 1 Is a degree any fixed or defi- 
nite quantity 1 What is the axis of a circle ? What is the pole 
of a circle ? How do all great circles cut each other? How- 
is a great circle cut by another great circle passing through its 
pole ? What is the secondary of a circle ? How is the angle 
madeby two great circles on the surface of the sphere measured? 

1 1 . How arc the earth and the heavens conceived to be di- 
vided ? What constitutes the terrestrial sphere ? What the 
celestial ? Have these circles any existence in nature ? In 
what do the heavenly bodies appear to be fixed ? 



DOCTRINE OF THE SPHERE. 11 

ence. On account of the immense distance of the heav- 
enly bodies, they appear to us, wherever we are placed, 
to be fixed in the same concave surface, or celestial 
vault. The great circles of the globe, extended every 
way to meet the concave surface of the heavens, become 
circles of the celestial sphere. 

12. The Horizon is the great circle which divides 
the earth into upper and lower hemispheres, and sepa- 
rates the visible heavens from the invisible. This is 
the rational horizon. The sensible horizon, is a circle 
touching the earth at the place of the spectator, and is 
bounded by the line in which the earth and skies seem 
to meet. The sensible horizon is parallel to the ra- 
tional, but is distant from it by the semi-diameter of the 
earth, or nearly 4,000 miles. Still, so vast is the dis- 
tance of the starry sphere, that both these planes appear 
to cut that sphere in the same line ; so that we see the 
same hemisphere of stars that we should see if the up- 
per half of the earth were removed, and we stood on the 
rational horizon. 

13. The poles of the horizon are the zenith and na- 
dir. The Zenith is the point directly over our head, 
and the Nadir that directly under £>ur ieeX. The plumb 
line is in the axis of the horizon, and consequently di- 
rected towards its poles. 

Every place on the surface of the earth has its own 
horizon ; and the traveller has a new horizon at every 
step, always extending 90 degrees from him in all di- 
rections. 



12. Define the Iwrizon. Distinguish between the rational 
and the sensible horizon. What is the distance between the 
sensible and rational horizons ? How do both appear to cut 
the starry heavens ? 

13. What are the poles of the horizon ? Define the zenith. 
Define the nadir. How is the plumb line situated with respec . 
to the horizon? How manv horizons are there on the earth ? 



12 THE EARTH. 

14. Vertical circles are those which pass through the 
poles of the horizon, perpendicular to it. 

The Meridian is that vertical circle which passes 
through the north and south points. 

The Prime Vertical, is that vertical circle which 
passes through the east and west points. 

The Altitude of a body, is its elevation above the ho- 
rizon, measured on a vertical circle. 

The Azimuth of a body, is its distance measured on 
the horizon from the meridian to a vertical circle passing 
through the body. 

The Amplitude of a body, is its distance on the hori- 
zon, from the prime vertical, to a vertical circle passing 
through the body. 

Azimuth is reckoned 90° from either the north or 
south point ; and amplitude 90° from either the east or 
west point. Azimuth and amplitude are mutually com- 
plements of each other. \Yhen a point is on the hori- 
zon, it is only necessary to count the number of degrees 
of the horizon between that point and the meridian, in 
order to find its azimuth ; but if the point is above the 
horizon, then its azimuth is estimated by passing a ver- 
tical circle through it, and reckoning the azimuth from 
the point w^here this circle cuts the horizon. 

The Zenith Distance of a body is measured on a ver- 
tical circle, passing through that body. It is the com- 
plement of the altitude. 

15. The Axis of the Earth is the diameter, on which 
the earth is conceived to turn in its diurnal revolution. 
The same line continued until it meets the starry con- 
cave, constitutes the axis of the celestial sphere. 



14. Define vertical circles — the meridian — lYiQ prime verti' 
cal — altitude — azimuth — amplitude. How many degrees of 
azimuth are reckoned ? from what points ? How are azimuth 
and amplitude related to each other ? Define zenith distance 
— How is it related to the altitude ? 

15. Define the axis of the earth — the axis of the celestial 
sphere — the poles of the earth — the poles of the heavens. 



DOCTRIXE OF THE SPHERE. 13 

The Poles of the Earth are the extremities of the 
earth's axis : the Poles of the Heavens, the extremities 
of the celestial axis. 

16. The Equator is a great circle cutting the axis of 
the earth at right angles. Hence the axis of the earth 
is the axis of the equator, and its poles are the poles of 
the equator. The intersection of the plane of the equa- 
tor with the surface of the earth, constitutes the terres- 
trial, and with the concave sphere of the heavens, the 
celestial equator. The latter, by way of distinction, is 
sometimes denominated the equinoctial. 

17. The secondaries to the equator, that is, the great 
circles passing through the poles of the equator, are 
called Meridians, because that secondary which passes 
through the zenith of any place is the meridian of that 
place, and is at right angles both to the equator and the 
horizon, passing as it does through the poles of both. 
These secondaries are also called Hour Circles, because 
the arcs of the equator intercepted between them are 
used as measures of time. 

18. The Latitude of a place on the earth, is its dis- 
tance from the equator north or south. The Polar Dis- 
tance, or angular distance from the nearest pole, is the 



19. The Longitude of a place is its distance from 
some standard meridian, either east or west, measured 
on the equator. The meridian usually taken as the 
standard, is that of the Observatory of Greenwich, in 
London. If a place is directly on the equator, we have 
only to inquire how many degrees of the equator there 



16. Define the equator. What constitutes the terrestrial 
equator ? what the celestial equator ? Whatis this also called? 

17. What are the secondaries of the equator called "^ 

18. Define the Latitude of a place — the polar distance, 

2 



14 THE EARTH. 

are between that place and the point where the meridian 
of Greenwich cuts the equator. If the place is north or 
south of the equator, then its longitude is the arc of the 
equator intercepted between the- meridian which passes 
through the place, and the meridian of Greenwich. 

20. The Ecliptic is a great circle in which the earth 
performs its annual revolution around the sun. It passes 
through the center of the earth and the center of the 
sun. It is found by observation that the earth does not 
lie with its axis at right angles to the plane of the eclip- 
tic, but that it is turned about 23J degrees out of a per- 
pendicular direction, making an angle with the plane 
itself of QQ^"". The equator, therefore, must be turned 
the same distance out of a coincidence with the ecliptic, 
the two circles making an angle with each other of 23J°. 
It is particularly important for the learner to form cor- 
rect ideas of the ecliptic, and of its relations to the equa- 
tor, since to these two circles a great number of astro- 
nomical measurements and phenomena are referred. 

21. The Equinoctial Points, or Equinoxes* are the 
intersections of the ecliptic and equator. The time 
when the sun crosses the equator in going northward 
is called the vernal, and in returning southward, the au- 
tumnal equinox. The vernal equinox occurs about 
the 21st of March, and the autumnal the 22d of Sep- 
tember. 



19. Define the Longitude of a place. What is the standard 
meridian ? When a place is on the equator, how is its longi- 
tude measured? how when it is north or south of the equator? 

20. Define the ecliptic. How does it pass with respect to 
the earth and the sun ? How is it situated with respect to the 
equator ? 

21. Define the equinoctial points. When is the vernal equi- 
nox, and when the autumnal ? 



* The term Equinoxes strictly denotes the times when the sun ar- 
rives at the equinoctial points, but it is frequently used to denote those 
points themselves. 



DOCTRINE OF THE SPHERE. 15 

22. The Solstitial Points are the two points of the 
ediptic most distant from the equator. The times when 
the sun comes to them are called solstices. The sum- 
mer solstice occurs about the 22d of June, and the win- 
ter solstice about the 22d of December. 

The ecliptic is divided into twelve equal parts of 30° 
each, called signs, which, beginning at the vernal equi- 
nox, succeed each other in the following order : 





Northern. 






Southern. 




1. 


Aries 


cp 


7. 


Libra 


^ 


2. 


Taurus 


« 


8. 


Scorpio 


m 


3. 


Gemini 


n 


9. 


Sagittarius 


f 


4. 


Cancer 


® 


10. 


Capricornus 


y9 


5. 


Leo 


a 


11. 


Aquarius 


^ 


6. 


Virgo 


n 


12. 


Pisces 


^ 



The mode of reckoning on the ecliptic, is by signs, de- 
gi'ees, minutes, and seconds. The sign is denoted either 
by its name or its number. Thus 100° may be express- 
ed either as the 10th degree of Cancer, or as 3^ 10°. 

23. Of the various meridians, two are distinguished 
by the name of Colures. The Equinoctial Colure, is 
the meridian which passes through the equinoctial 
points. From this meridian, right ascension and celes- 
tial longitude are reckoned, as longitude on the earth is 
reckoned from the meridian of Greenwich. The Sol- 
stitial Colure, is the meridian which passes through the 
solstitial points. 

24. The position of a celestial body is referred to the 
equator by its right ascension and declination. Right 



22. Define the solstitial points, and solstices. When does 
the summer solstice occur ? when does the winter solstice oc- 
cur ? Into how many signs is the ecliptic divided? How 
many degrees are there in each ? Name the signs. What is 
the mode of reckoning on the ecliptic ? In what two wa,vs 
may 100^ be expressed? 

23. What is the equinoctial colure ? — the solstitial colure ? 



16 THE EARTH. 

Ascension, is the angular distance from the vernal equi- 
nox measured on the equator. If a star is situated on 
the equator, then its right ascension is the number of 
degrees of the equator between the star and the vernal 
equinox. But if the star is north or south of the equa- 
tor, then its right ascension is the arc of the equator, in- 
tercepted between the vernal equinox and that secon- 
dary to the equator w^hich passes through the star. De- 
clination is the distance of a body from the equator, 
measured on a secondary to the latter. Therefore, right 
ascension and declination correspond to terrestrial longi- 
tude and latitude, right ascension being reckoned from 
the equinoctial colure, in the same manner as longitude 
is reckoned from the meridian of Greenwich. On the 
other hand, celestial longitude and latitude are referred, 
not to the equator, but to the ecliptic. Celestial Longi- 
tude, is the distance of a body from the vernal equinox 
reckoned on the ecliptic. Celestial Latitude, is distance 
from the ecliptic measured on a secondary to the latter. 
Or, more briefly. Longitude is distance on the eclip- 
tic ; Latitude, distance from the ecliptic. The Noi^th 
Pola?^ Distance of a star, is the complement of its de- 
chnation. 

25. Parallels of Latitude are small circles parallel to 
the equator. They constantly diminish in size as we go 
from the equator to the pole. 

The Tropics are the parallels of latitude that pass 
through the solstices. The northern tropic is called the 
tro])ic of Cancer ; the southern, the tropic of Capricorn. 

The Polar Circles are the parallels of latitude that 
pass through the poles of the ecliptic, at the distance of 
23J degrees from the pole of the earth. 



24. Define right ascension and declination. To what do 
they correspond on the terrestrial sphere 1 Define celestial 
longitude and latitude. 

25. What are parallels of latitude — tropics — polar circles ? 
To what is the elevation of the pole always equal ? also that 
of the equator ? 



DOCTRINE OF THE SPHERE. 17 

The elevation of the pole of the heavens above the 
horizon of any place, is always equal to the latitude of 
the place. Thus, in 40° of north latitude we see the 
north star 40° above the northern horizon, whereas, if 
we should travel southw^ard its elevation would grow 
less and less, until we reached the equator, where it 
w^ould appear in the horizon ; or, if w^e should travel 
northward, the north star would rise constantly higher 
and higher, until, if we could reach the pole of the earth, 
that star w^ould appear directly over head. The eleva- 
tion of the equator above the horizon of any place, is 
equal to the complement of the latitude. Thus, at the 
latitude of 40° N. the equator is elevated 50° above the 
southern horizon. 

26. The earth is divided into five zones. That por- 
tion of the earth which lies between the tropics, is called 
the Torrid Zone : that between the tropics and polar 
circles, the Temperate Zones; and that between the 
polar circles and the poles, the Frigid Zones. 

27. The Zodiac is the part of the celestial sphere, 
v/hich lies about 8 degrees on each side of the ecliptic. 
This portion of the heavens is thus marked off by itself^ 
because all the planets move within it. 

28. After endeavoring to form, from the definitions, 
as clear an idea as he can of the various circles of the 
sphere, the learner may next resort to an artificial globe, 
and see how they are severally represented there. Or if 
he has not access to a globe, he may aid his conceptions 
by the following easy device. To represent the earth, 
select a large apple^ (a melon when in season will be 
found still better.) The shape of the apple, flattened as 



26. Define each of the zones. 

27. Define the zodiac. 

28. Show how to represent the artificial sphere by any round 
body, as an apple, and point out the various circles on it, 

2* 



18 THE EARTH. 

it usually is at the two ends, will not inaptly exhibit 
the spheroidal figure of the earth, while the larger diam- 
eter through the middle will indicate the excess of mat- 
ter about the equator ; although we should remark, that 
the disproportion between the polar and equatorial diam- 
eters of the earth is in fact so slight, that it would be 
scarcely perceptible in a model. The eye and the stem 
of the apple will indicate the position of the two poles 
of the earth. Applying the thumb and finger of the 
left hand to the poles, and holding the apple so that the 
poles may be in a north and south line, turn the globe 
from west to east, and its motion will correspond to the 
diurnal movement of the globe. Pass a wire, as a knit- 
ting needle, through the poles, and it will represent the 
axis of the sphere. A circle cut around the apple half 
way between the poles, will be the equator ; and several 
other circles cut between the equator and the poles, par- 
allel to the equator, will represent parallels of latitude, 
of which, two drawn 23J degrees from the equator, will 
be the tropics, and two others at the same distance from 
the poles, will be the polar circles. A great circle cut 
through the poles in a north and south direction, will 
form the meridian, and several other great circles drawn 
through the poles, and of course perpendicularly to the 
equator, will be secondaries to the equator, constituting 
meridians or hour circles. A great circle cut through the 
center of the earth from one tropic to the other, will rep- 
resent the plane of the ecliptic, and consequently, a line 
cut around the apple where such a section meets the sur- 
face, is the terrestrial ecliptic. The points where this 
circle meets the tropics, are the solstices, and its intersec- 
tions with the equator are the equinoctial points. 

29. The horizon is best represented by a circular 
piece of pasteboard, cut so as to fit closely to the apple, 
being movable upon it. When this horizon is slipped 

29. How is the horizon represented in our model ? How is 
it placed to represent the horizon of the equator ? How for the 
horizon of the poles ? How for our own horizon 1 How shall 
we represent the prime vertical ? 



DOCTRINE OF THE SPHERE. 19 

up to the poles, it becomes the horizon of the equator ; 
when it is so placed as to coincide with the earth's 
equator, it becomes the horizon of the poles ; and in 
every other situation it represents the horizon of a place 
on the globe 90° every way from it. Suppose we are 
in latitude 40°, then let us place our movable paper par- 
allel to our own horizon, and elevate the pole 40° above 
it, as near as we can judge by the eye. If we cut a cir- 
cle around the apple, passing through its highest parts 
and through the east and west points, it will represent 
the prime vertical. 

30. We cannot too strongly recommend to the young 
learner to form for himself such a sphere as is here de- 
scribed, and to point out on it the various arcs of azimuth 
and altitude, right ascension and declination, terrestrial 
and celestial latitude and longitude, these last being re^ 
ferred to the equator on the earth, and to the ecliptic ii^ 
the heavens. 

31. When the circles of the sphere are well learned, 
we may advantageously employ projections of them in 
various illustrations. By the projection of the sphere is 
meant a representation of all its parts on a plane. The 
plane itself is called the plane of projection. Let us take 
any circular ring, as a wire bent into a circle, and hold 
it in different positions before the eye. If we hold it 
parallel to the face, or directly opposite to the eye, we 
see it as an entire circle. If we turn it a little sideways, 
it appears oval, or as an ellipse ; and as we continue to 
turn it more and more round, the ellipse grows narrower 
and narrower, until, when the edge is presented to the 
eye, we see nothing but a line. Now imagine the ring 
to be near a perpendicular wall, and the eye to be re- 



30. Whatis particularly recommended to the young learner? 

31 What is meant by the projection of the sphere ? What 
is the projection of a circle when seen directly before the face ? 
what when seen obliquely 1 what when seen edgewise ? 



I 



20 



THE EARTH. 



moved at such a distance from it, as not to distinguish 
any interval between the ring and the wall ; then the 
several figures under which the ring is seen, will appear 
to be inscribed on the wall, and we shall see the ring as 
a circle when perpendicular to a straight line joining 
the center of the ring and the eye, as an ellipse when 
oblique to this line, or as a straight line when its edge is 
towards us. 

32. It is in this manner that the circles of the sphere 
are projected, as represented in the following diagram 




Here various circles are represented as projected on the 
meridian, which is supposed to be situated directly be- 
fore the eye, at some distance from it. The horizon HO 
being perpendicular to the meridian is seen edgewise, and 
consequently is projected into a straight line. The same 
is the case with the prime vertical ZN, with the equator 
EQ, and the several small circles parallel to the equator, 
which represent the two tropics and the two polar cir- 



32. In. figure 5, what represents the plane of projection ? 
Why are certain circles represented by straight lines ? why are 
others represented by eUipses ? How is the eye supposed to 
be situated ? 



DIURNAL REVOLUTION. 21 

cles. In fact, all circles whatsoever, which are perpen- 
dicular to the plane of projection, will be represented 
by straight lines. But every circle which is perpendic- 
ular to the horizon, except the prime vertical, being seen 
obhquely as ZMN, will be projected into an elhpse. 
In the same manner, PRP, an hour circle, being oblique 
to the eye, is represented by an ellipse on the plane of 
projection. 



CHAPTER II. 

DIURNAL REVOLUTION ARTIFICIAL GLOBES. 

33. The apparent diurnal revolution of the heavenly 
bodies from east to west, is owing to the actual revolu- 
tion of the earth on its own axis from west to east., Ii 
we conceive of a radius of the earth's equator extended 
until it meets the concave sphere of the heavens, then 
as the earth revolves, the extremity of this line would 
trace out a curve on the face of the sky, namely, the ce- 
lestial equator. In curves parallel to this, called the cir- 
cles of diurnal revolution, the heavenly bodies actually 
appear to move, every star having its own peculiar cir- 
cle. After the learner has first rendered familiar the 
real motions of the earth from west to east, he may 
then, without danger of misconception, adopt the com- 
mon language, that all the heavenly bodies revolve 
around the earth once a day from east to west, in circles 
parallel to the equator and to each other. 

34. The time occupied by a star in passing from any 
point in the meridian until it comes round to the same 



33. To what is the apparent diurnal revolution of the heav- 
enly bodies from east to west owing ? If a radius of the earth's 
equator were extended to meet the concave sphere of the heav- 
ens, what would it trace out as the earth revolves ? What 
are circles of diurnal revolution ? 



22 THE EARTH. 

point again, is called a sidereal day, and measures the 
period of the earth's revolution on its axis. If we watch 
the returns of the same star from day to day, we shall 
find the intervals exactly equal to one another ; that is, 
the sidereal days are all equal. Whatever star we se- 
lect for the observation, the same result will be obtained. 
The stars, therefore, always keep the same relative posi- 
tion, and have a common movement round the earth — 
a consequence that naturally flows from the hypothesis, 
that their apparent motion is all produced by a single 
real motion, namely, that of the earth. The sun, moon, 
and planets, as well the fixed stars, revolve in like man- 
ner, but their returns to the meridian are not, like those 
of the fixed stars, at exactly equal intervals. 

35. The appearances of the diurnal motions of the 
^ heavenly bodies are different in different parts of the 
earth, since every place has its own horizon, (Art. 8,) 
and different horizons are variously inclined to each 
other. Let us suppose the spectator viewing the diurnal 
revolutions from several different positions on the earth. 

On the equator, his horizon would pass through both 
poles ; for the horizon cuts the celestial vault at 90 de- 
grees in every direction from the zenith of the spectator ; 
but the pole is likewise 90 degrees from his zenith, and 
consequently, the pole must be in the horizon. The ce- 
lestial equator would coincide with the Prime Vertical, 



34. Define a sidereal day. Are the sidereal days equal or 
unequal ? Are the returns of the sun, moon, and planets to 
the meridian, likewise at equal intervals ? 

35. How are the appearances of the diurnal motions in dif- 
ferent parts of the earth ? When the spectator is on the equa- 
tor, where would his horizon pass with respect to the poles of 
the earth? With what great circle would the celestial equator 
coincide ? How would all the circles of diurnal revolution be 
situated with respect to the horizon ? Define a right sphere. 
In a right sphere, how would a star situated in the celestial 
equator perform its circuit ? how would stars nearer the poles 
appear to move ? 



DIURNAL REVOLUTION. 23 

being a great circle passing through the east and west 
points. Since all the diurnal circles are parallel to the 
equator, consequently, they would all, like the equator, 
be perpendicular to the horizon. Such a view of the 
heavenly bodies, is called a right sphere ; or, 

A Right Sphere is one in which all the daily revolu- 
tions of the stains, are in circles perpendicular to the horizon. 

A right sphere is seen only at the equator. Any star 
situated in the celestial equator, w^ould appear to rise di- 
rectly in the east, when on the meridian to be in the 
zenith of the spectator, and to set directly in the West ; 
in proportion as stars are at a greater distance from the 
equator towards the pole, they describe smaller and 
smaller circles, until, near the pole, their motion is hardly 
perceptible. 

36. If the spectator advances one degree towards the 
north pole, his horizon reaches one degree beyond the 
pole of the earth, and cuts the starry sphere one degree 
below the pole of the heavens, or below the north star, 
if that be taken as the place of the pole. As he moves 
onward towards the pole, his horizon continually reaches 
farther and farther beyond it, until when he comes to 
the pole of the earth, and under the pole of the heavens, 
his horizon reaches on all sides to the equator and coin- 
cides with it. Moreover, since all the circles of daily 
motion are parallel to the equator, they become, to the 
spectator at the pole, parallel to the horizon. This is 
v^fhat constitutes a parallel sphere. Or, 

A Parallel Sphere is that in lohich all the circles of 
daily motion are parallel to the horizon. 

To render this view of the heavens familiar, the 
learner should follow round in his mind a number of 



36. What changes take place in one's horizon as he moves 
from the equator towards the pole ? How would it be situated 
when he reached the pole 1 Define a parallel sphere. Explain 
the appearances of the stars and of the sun in a parallel sphere. 
Where only can such a sphere be seen 1 Has the pole of the 
earth ever been reached by man ? 



24 THE EARTH. 

separate stars, one near the horizon, one a few degrees 
above it, and a third near the zenith. To one who 
stood upon the north pole, the stars of the northern hemi- 
sphere would all be perpetually in view when not ob- 
scured by clouds or lost in the sun's light, and none of 
those of the southern hemisphere would ever be seen. 
The sun would be constantly above the horizon for six 
months in the year, and the remaining six constantly 
out of sight. That is, at the pole the days and nights 
are each six months long. The phenomena at the south 
pole are similar to those at the north. 

A perfect parallel sphere can never be seen except at 
one of the poles — a point which has never been actually 
reached by man ; yet the British discovery ships pene- 
trated within a few degrees of the north pole, and of 
course enjoyed the view of a sphere nearly parallel. 

37. As the circles of daily motion are parallel to the 
horizon of the pole, and perpendicular to that of the 
equator, so at all places between the two, the diurnal 
motions are oblique to the horizon. This aspect of the 
heavens constitutes an oblique sphere, which is thus de- 
fined : 

An Oblique Sphere is that in which the circles of 
daily motion are oblique to the horizon. 

Suppose, for example, the spectator is at the latitude of 
fifty degrees. His horizon reaches 50° beyond the pole 
of the earth, and gives the same apparent elevation to 
the pole of the heavens. It cuts the equator, and all 
the circles of daily motion, at an angle of 40°, being al- 
ways equal to the co-altitude of the pole. Thus, let HO 
(Fig. 6,) represent the horizon, EQ the equator, and 
PP' the axis of the earth. Also, //, mm, &:c., parallels 
of latitude. Then the horizon of a spectator at Z, in 
latitude 50° reaches to 50° beyond the pole ; and the 
angle ECH, is 40°. As we advance still farther north 



37. Define an oblique sphere. Where is it seen ? At the 
latitude of 50° how is the horizon situated ? Illustrate by fig. 6 



DIURNAL REVOLUTION. 

Fig. 6. 
Z 



25 





^ 


"^ 


[ -. 




y 


y^.. 








A 


•.. 


■•■.. 


J 


':. \ 


^ 






y/\ 




K 




■V r 


"/^-^ 


\ \ 


'm — -^ 




^ 






1^'\ 




\/ 


\. 


"^ "\] 


V\ 


^ 


'\ 







the elevation of the diurnal circles grows less and less, 
and consequently the motions of the heavenly bodies 
more and more oblique, until finally, at the pole, where 
the latitude is 90°, the angle of elevation of the equator 
vanishes, and the horizon and equator coincide with 
each other, as before stated. 

38. The CIRCLE of perpetual apparition, is the 

boundary of that space around the elevated pole, where 
the stars never set. Its distance from the pole is equal 
to the latitude of the place. For, since the altitude of 
the pole is equal to the latitude, a star whose polar dis- 
tance is just equal to the latitude, will when at its low- 
est point only just reach the horizon ; and all the stars 
nearer the pole than this will evidently not descend so 
far as the horizon. 

Thus, mm (Fig. 6,) is the circle of perpetual appari- 
tion, between which and the north pole, the stars never 
set, and its distance from the pole OP is evidently equal 
to the elevation of the pole, and of course to the lati- 
tude. 



38. What is the circle of perpetual apparition ? 
by fig. 6. 

3 



Llustrate 



26 THE EARTH. 

39. In the opposite hemisphere, a similar part of the 
sphere adjacent to the depressed pole never rises. Hence, 

The CIRCLE OF PERPETUAL occuLTATioN, is the boun- 
dary of that space around the depressed pole, within 
which the stars never rise. Thus, m'?n (Fig. 6,) is the 
circle of perpetual occultation, between which and the 
south pole, the stars never rise. 

40. In an obHque sphere, the horizon cuts the circles 
of daily motion unequally. Towards the elevated pole, 
more than half the circle is above the horizon, and a 
greater and greater portion as the distance from the 
equator is increased, until finally, within the circle of 
perpetual apparition, the whole circle is above the hori- 
zon. Just the opposite takes place in the hemisphere 
next the depressed pole. Accordingly, when the sun is 
in the equator, as the equator and horizon, like all other 
great circles of the sphere, bisect each other, the days 
and nights are equal all over the globe. But when the 
sun is north of the equator, the days become longer than 
the nights, but shorter when the sun is south of the 
equator. Moreover, the higher the latitude, the greater 
is the inequality in the lengths of the days and nights. 
All these noints will be readily understood by inspecting 
figure 6 

41. Most of the appearances of the diurnal revolution 
can be explained, either on the supposition that the ce- 
lestial sphere actually all turns around the earth once in 
24 hours, or that this motion of the heavens is merely 
apparent, arising from the revolution of the earth on its 



39. What is the circle of perpetual occultation ? Illustrate 
by fig. 6. 

40. How does the horizon of an oblique sphere cut the cir- 
cles of daily motion ? Towards the elevated pole what portion 
of the circles is above the horizon ? Towards the depressed 
pole, how is the fact ? When are the days and nights equal 
all over the world ? When are the days longer, and when 
shorter than the nights ? 



DIURNAL REVOLUTION. 27 

axis in the opposite direction — a motion of which we 
are insensible, as we sometimes lose the consciousness 
of our own motion in a ship or a steamboat, and observe 
all external objects to be receding from us with a com- 
mon motion. Proofs entirely conclusive and satisfac- 
tory, establish the fact, that it is the earth and not the 
celestial sphere that turns ; but these proofs are drawn 
from various sources, and. the student is not prepared to 
appreciate their value, or even to understand some of 
them, until he has made considerable proficiency in the 
study of astronomy, and become familiar with a great 
variety of astronomical phenomena. To such a period 
of our course of instruction, we therefore postpone the 
discussion of the hypothesis of the earth's rotation on 
its axis. 

42. While we retain the same place on the earth, the 
diurnal revolution occasions no change in our horizon, 
but our horizon goes round as well as ourselves. Let 
us first take our station on the equator at sunrise ; our 
horizon now passes through both the poles, and through 
the sun, which we are to conceive of as at a great dis- 
tance from the earth, and therefore as cut, not by the 
terrestrial but by the celestial horizon. As the earth 
turns, the horizon dips more and more below the sun, at 
the rate of 15 degrees for every hour, and, as in the case 
of the polar star, the sun appears to rise at the same rate. 
In six hours, therefore, it is depressed 90 degrees below 
the sun, which brings us directly under the sun, which, 
for our present purpose, we may consider as having all 
the w^hile maintained the same fixed position in space. 



41 . On what suppositions can the appearances of the diurnal 
revolution be explained ? Is it the earth or the heavens that 
really move ? Why is the discussion of this subject postponed ? 

42. Explain the true cause of the sun's appearing to rise and 
set, as observed at the equator. What is the position of the ho- 
rizon at sunrise ? What at six hours afterwards ? What at 
the end of twelve hours ? What at the end of eighteen hours ? 



28 THE EARTH. 

The earth continues to turn, and in six hours more, it 
completely reverses the position of our horizon, so that 
the western part of the horizon which at sunrise was 
diametrically opposite to the sun now cuts the sun, and 
soon afterwards it rises above the level of the sun, and 
the sun sets. During the next twelve hours, the sun 
continues on the invisible side of the sphere, until the 
horizon returns to the position from which it started, and 
a new day begins. 

43. Let us next contemplate the similar phenomena 
at the poles. Here the horizon, coinciding as it does 
with the equator, would cut the sun through its center, 
and the sun w^ould appear to revolve along the surface 
of the sea, one-half above and the other half below the 
horizon. This supposes the sun in its annual revolution 
to be at one of the equinoxes. When the sun is north 
of the equator, it revolves continually round in a circle, 
which, during a single revolution, appears parallel to the 
equator, and it is constantly day ; and when the sun 
is south of the equator, it is, for the same reason, contin- 
ual night. 

We have endeavored to conceive of the manner in 
w^hich the apparent diurnal movements of the sun are 
really produced at two stations, namely, in the right 
sphere, and in the parallel sphere. These two cases 
being clearly understood, there will be little difficulty in 
applying a similar explanation to an oblique sphere. 



ARTIFICIAL GLOBES. 

44. Artificial globes are of two kinds, terrestrial and 
celestial. The first exhibits a miniature representation 
of the earth ; the second, of the visible heavens ; and 
both show the various circles by which the two spheres 



43. Explain the similar phenomena at the poles, first, when 
the sun is at the equinoxes, and secondly, when it is north and 
when it is south of the equator. 



ARTIFICIAL GLOBES. 29 

are respectively traversed. Since all globes are similar 
solid figures, a small globe, imagined to be situated at 
the center of the earth or of the celestial vault, may rep- 
resent all the visible objects and artificial divisions of 
either sphere, and with great accuracy and just propor- 
tions, though on a scale greatly reduced. The study of 
artificial globes, therefore, cannot be too strongly recom- 
mended to the student of astronomy.* 

45. An artificial globe is encompassed from north to 
south by a strong brass ring to represent the meridian of 
the place. This ring is made fast to the two poles and 
thus supports the globe, while it is itself supported in a 
vertical position by means of a frame, the ring being 
usually let into a socket in which it may be easily slid, 
so as to give any required elevation to the pole. The 
brass meridian is graduated each way from the equator 
to the pole 90°, to measure degrees of latitude or decli- 
nation, according as the distance from the equator refers 
to a point on the earth or in the heavens. The horizon 
is represented by a broad zone, made broad for the con- 
venience of carrying on it a circle of azimuth, another of 
amplitude, and a wide space on which are delineated 
.the signs of the ecliptic, and the sun's place for every 
day in the year ; not because these points have any spe- 
cial connexion with the horizon, but because this broad 
surface furnishes a convenient place for recording them. 



44. What does the terrestrial globe exhibit 1 What does 
the celestial globe ? What do both show ? 

45. How is the meridian of the place represented? To what 
points is the brass meridian fastened ? What supports the ring 1 
How is it graduated 1 How is the horizon represented ? Why 
is it made broad ? What circles are inscribed on it 1 



* It were desirable, indeed, that every student of the science should 
have a celestial globe, at least, constantly before him. One of a 
small size, as eight or nine inches, will answer the purpose, although 
globes of these dimensions cannot usually be relied on for nice meas- 
urements 

3* 



30 THE EARTH. 

46. Hour Circles are represented on the terrestrial 
globe by great circles drawn through the pole of the 
equator ; but, on the celestial globe, corresponding cir- 
cles pass through the poles of the ecliptic, constituting 
circles of latitude, while the brass meridian, being a se- 
condary to the equinoctial, becomes an hour circle of 
any star which, by turning the globe, is brought under it. 

47. The Hour Index is a small circle described around 
the pole of the equator, on which are marked the hours 
of the day. As this circle turns along with the globe, it 
makes a complete revolution in the same time with the 
equator ; or, for any less period, the same number of de- 
grees of this circle and of the equator pass under the 
meridian. Hence the hour index measures arcs of right 
ascension, 15° passing under the meridian every hour. 

48. The Quadrant of Altitude is a flexible strip of 
brass, graduated into ninety equal parts, corresponding 
in length to degrees on the globe, so that w^hen applied to 
the globe and bent so as closely to fit its surface, it meas- 
ures the angular distance between any two points. 
When the zero, or the point where the graduation be- 
gins, is laid on the pole of any great circle, the 90th de- 
gree will reach to the circumference of that circle, and 
being therefore a great circle passing through the pole 
of another great circle, it becomes a secondary to the 
latter. Thus the quadrant of altitude may be used as a 
secondary to any great circle on the sphere ; but it is 
used chiefly as a secondary to the horizon, the point 



46. How are hour circles represented on the terrestrial 
globe ? How are circles of latitude represented on the celes- 
tial globe ? 

47. Describe the hour index. What does it measure ? 

48. What is the quadrant of altitude? How is it gradua- 
ted 1 When the zero point is laid on the pole of any great cir- 
cle, to what will the 90th degree reach ? How may it be used 
as a secondary to any great circle ? When screwed on the 
zenith what does it become 1 What arcs does it then measure ? 



TERRESTRIAL GLOBE. 31 

marked 90° being screwed fast to the pole of the hori- 
zon, that is, the zenith, and the other end, marked 0, 
being sHd along between the surface of the sphere and 
the wooden horizon. It thus becomes a vertical circle, 
on which to measure the altitude of any star through 
which it passes, or from which to measure the azimuth 
of the star, w^iich is the arc of the horizon intercepted 
between the meridian and the quadrant of altitude pass- 
ing through the star. 

49. To rectify the. globe for any place, the north pole 
must be elevated to the latitude of the place ; then the 
equator and all the diurnal circles will have their due in- 
clination in respect to the horizon ; and, on turning the 
globe, every point on either globe will revolve as the 
same point does in nature ; and the relative situations of 
all places will be the same as on the native spheres. 

PROBLEMS ON THE TERRESTRIAL G]W>BE. 

50. To find the Latitude and Longitude of a place : 
Turn the globe so as to bring the place to the brass me- 
ridian ; then the degree and minute on the meridian di- 
rectly over the place will indicate its latitude, and the 
point of the equator under the meridian, will show its 
longitude. 

Ex. What is the Latitude and Longitude of the city 
of New York ? 

51. To find a place having its Latitude and Longitude 
given : Bring to the brass meridian the point of the equa- 
tor corresponding to the longitude, and then at the de- 
gree of the meridian denoting the latitude, the place will 
be found. 

Ex. What place on the globe is in Latitude 39° N. and 
Longitude 77° W. ? 



49. How do we rectify the globe for any place ? 

50. Find the latitude and longitude of Washington City. 

51. What place lies in latitude 39° N. and longitude 77° W.I 



32 THE EARTH. 

52. To find the hearing and distance of two places : 
Ii^ectify the globe for one of the places ; screw the quad- 
rant of altitude to the zenith,* and let it pass through 
the other place. Then the azimuth will give the bear- 
ing of the second place from the first, and the number 
of degrees on the quadrant of altitude, multiplied by 69, 
(the number of miles in a degree,) will give the distance 
between the two places. 

Ex. What is the bearing of New Orleans from New 
York, and what is the distance between these places ? 

53. To determine the difference of time in different 
places : Bring the place that lies eastward of the other 
to the meridian, and set the hour index at XII. Turn 
the globe eastward until the other place comes to the 
meridian, then the index will point to the hour required. 

Ex. When it is noon at New York, what time is it at 
London ? 

54. The hour being given at any place, to tell what 
hour it is in any other part of the world : Bring the 
given place to the meridian, and set the hour index to 
the given time ; then turn the globe, until the other 
place comes under the meridian, and the index will 
point to the required hour. 

Ex. What time is it at Canton, in China, when it is 
9 o'clock A. M. at New York ? 

55. To find what people on the earth live under us, 
having their noon at the time of our midnight : Bring 
the place where we dwell to the meridian, and set the 



52. What is the bearing and distance of New Orleans from 
New York ? 

53. When it is noon at New York, what time is it at Pekin ? 

54. What time is it at London when it is noon at Boston 1 



* The zenith will of course be the point of the meridian over the 
place. 



TERRESTRIAL GLOBE. 33 

hour index to XII ; then turn the globe until the other 
XII comes under the meridian; the point under the 
same part of the meridian where we were before, will 
be the place sought. 

Ex. Find what place is directly under New York. 

56. To find what people of the southern heinisphere 
are directly opposite to us : Bring our place to the me- 
ridian ; the place in the same latitude south, then un- 
der the meridian, will be the place in question. 

Ex. What place in the southern hemisphere corres- 
ponds to New Haven ? 

57. To find the antipodes of a place, or the people 
lohosefeet are exactly opposite to ours : Bring our place 
to the meridian ; set the hour index to XII, and turn the 
globe until the other XII comes under the meridian ; 
then the point of the southern hemisphere under the me- 
ridian and having the same latitude with ours, will be 
the place of our antipodes. 

Ex. Who are antipodes to the people of Philadelphia ? 

58. To rectify the globe for the sun^s place : On the 
wooden horizon, find the day of the month, and against 
it is given the sun's place in the ecliptic, expressed by 
signs and degrees.* Look for the same sign and degree 
on the ecliptic, bring that point to the meridian and set 
the hour index to XII. To all places under the merid- 
ian it will then be noon. 

Ex. Rectify the globe for the sun's place on the 1st 
of September. 



55. Find what place is directly under Philadelphia. 

56. What place in south latitude corresponds to Boston '? 

57. Who are the antipodes of the people of London ? 

58. Rectify the globe for the sun's place for the first of June 



* The larger globes have the day of the month marked against the 
corresponding sign on the ecliptic itself. 



34 THE EARTH. 

59. Tne latitude of the place being given, to find the 
time of the sun's rising and setting on any given day 
at that place : Having rectified the globe for the lati- 
tude, bring the sun's place in the ecliptic to the gradua- 
ted edge of the meridian, and set the hear index to XII ; 
then turn the globe so as to bring the sun to the eastern 
and then to the western horizon, and the hour index 
will show the times of rising and setting respectively. 

Ex. At what time will the sun rise and set at New 
Haven, Lat. 41° 18', on the 10th of July ? 

PROBLEMS ON THE CELESTIAL GLOBE. 

60. To find the Declination and Right Ascension oj 
a heavenly body : Bring the place of the body (whether 
sun or star) to the meridian. Then the degree and 
minute standing over it will show its declination, and 
the point of the equinoctial under the meridian will give 
its right ascension. It will be remarked, that the decli- 
nation and right ascension are found in the same man- 
ner as latitude and longitude on the terrestrial globe. 
Right ascension is expressed either in degrees or in 
hours ; both being reckoned from the vernal equinox. 

Ex. What is the declination and right ascension of the 
bright star Lyra? — also of the sun on the 5th of June? 

61. To represent the appearance of the heavens at any 
time : Rectify the globe for the latitude, bring the sun's 
place in the ecliptic to the meridian, and set the hour 
index to XII ; then turn the globe westward until the 
index points to the given hour, and the constellations 
w^ould then have the same appearance to an eye situated 



59. Find the time of the sun's rising and setting at Boston 
(Lat. 42°, Lon. 71°) on the fast day of December. 

60. On the celestial globe, What is the right ascension and 
declination of any star taken at pleasure ? 

61. Represent the appearance of ihe heavens at Tuscaloosa 
(Lat. 33^, Lon. 87^) at 8 o'clock in the evening of Nov. 13th. 



CELESTIAL GLOBE. 35 

at the center of the globe, as they have at that moment 
in the sky. 

Ex. Required the aspect of the stars at New Haven, 
Lat. 4P 18', at 10 o'clock, on the evening of Decem- 
ber 5th. 

62. To find the altitude and azimuth of any star : 
Rectify the globe for the latitude, and let the quadrant 
of altitude be screwed to the zenith, and be made to pass 
through the star. The arc on the quadrant, from the 
horizon to the star, will denote its altitude, and the arc 
of the horizon from the meridian to the quadrant, will be 
its azimuth. 

Ex. What is the altitude and azimuth of Sirius (the 
brightest of the fixed stars) on the 25th of December at 
10 o'clock in the evening, in Lat. 41°? 

63. To find the angular distance of two stars from 
each other : Apply the zero mark of the quadrant of alti- 
tude to one of the stars, and the point of the quadrant 
which falls on the other star, will show the angular dis- 
tance between the two. 

Ex. What is the distance between the two largest 
stars of the Great Bear.* 

64. To find the sun^s meridian altitude, the latitude 
and day of the month being given : Having rectified 
the. globe for the latitude, bring the sun's place in the 
ecliptic to the meridian, and count the number of de- 



62. Find the altitude and azimuth of Lyra at 10 o'clock in 
the evening of June 18th, in Lat. 42°. 

63. Find the angular distance between any two stars taken 
at pleasure. 



* These two stars are sometimes called "the Pointers," from the line 
which passes through them heing always nearly in the direction of th' 
north star. The angular distance between them is about 5'=', and ma} 
be learned as a standard of reference in estimating by the eye, the dis- 
tance between any two points on the celestial vault. 



3:6 



THE EARTH. 



gre6s and minutes between that point of the meridian 
and the zenith. The complement of this arc will be 
the sun's meridian altitude. 

Ex. What is the sun's meridian altitude at noon on 
the 1st of August, in Lat. 41° 18"? 



CHAPTER III. 

OP PARALLAX, REFRACTION, AND TWILIGHT. 

65. Parallax is the apparent change of place which 
bodies undergo by being viewed from different points. 



Fig. 7. 




Thus in figure 7, let A represent the earth, CH the ho- 
rizon. HZ a quadrant of a great circle of the heavens. 



64. What is the sun's meridian altitude at noon on the 1 8th 
of June, in latitude 35° ? 

65. Define parallax. Illustrate by the figure. What angle 
measures the parallax? Why do astronomers consider the 
heavenly bodies as viewed from the center of the earth ? 



PARALLAX. 37 

extending from the horizon to the zenith ; and let E, F, 
G, O, be successive positions of the moon at different 
elevations, from the horizon to the meridian. Now a 
spectator on the sm'face of the earth at A, would refer 
the place of E to h, whereas, if seen from the center of 
the earth, it would appear at H. The arc HA is called 
the parallactic arc, and the angle HE/?, or its equal AEC, 
is the angle of parallax. The same is true of the angles 
at F, G, and O, respectively. 

Since then a heavenly body is Hable to be referred to 
different points on the celestial vault, Vvhen seen from 
different parts of the earth, and thus some confusion 
occasio-ned in the determination of points on the celes- 
tial sphere, astronomers have agreed to consider the true 
place of a celestial object to be that, w^here it would 
appear if seen from the center of the earth. The doc- 
trine of parallax teaches how to reduce observations 
made at any place on the surface of the earth, to such as 
they would be if made from the center. 

QQ. The angle AEC is called the horizonta parallax, 
which may be thus defined. Horizontal Parallax, is 
the change of position which a celestial body, appearing 
in the horizon as seen from the surface of the earth, 
would assume if viev\'ed from the earth's center. It is 
the angle subtended by the semi-diameter of the earth, 
as viewed from the body itself. 

It is evident from the figure, that the effect of parallax 
upon the place of a celestial body is to depress it. Thus, 
in consequence of parallax, E is depressed by the arc 
HA ; F by the arc Pp ; G by the arc Rr ; while O sus- 
tains no change. Hence, in all observations on the al- 
titude of the sun, moon, or planets, the amount of par- 
allax is to be added : the stars, as we shall see here- 
after, have no sensible parallax. 



66. Define horizontal parallax — By what is it subtended? 
(See Art. 10, Note) What is the effect of parallax upon the 
place of a heavenlv body? 

4 



38 



THE EARTH. 



67. The determination of the horizontal parallax of a 
celestial body is an element of great importance, since it 
furnishes the means of estimating the distance of the 
body from the center of the earth. Thus, if the angle 
AEC (Fig 7,) be found, the radius of the earth AC be- 
ing known, we have in the right angled triangle AEC, 
the side AC and all the angles, to find the side CE, 
which is the distance of the moon from the center ot 
the earth.* 

REFRACTION. 

68. While parallax depresses the celestial bodies sub- 
ject to it, refraction elevates them ; and it affects alike 
the most distant as well as nearer bodies, being occa- 
sioned by the change of direction which light undergoej* 

Fig. 8. 




67. Why is the determination of the parallax of a heavenly 
body an element of great importance ? Illustrate by figure 7. 



* Should the reader be unacquainted with the principles of trigonom- 
etry, yet he ought to know the fad that these principles enable us, 
when we have ascertained certain parts in a triangle, to find jthe un- 
known parts. Thus, in the above case, when we have found the an- 
gle of parallax, AEB, (which is determined by certain astronomical ob- 
servations,) knowing also the semi-diameter of the earth AC, we caa 
find by trigonometry, the length of the side CE, w^hich is tlie distance 
of the body from the center of the earth. 



REFRACTION. 39 

in passing through the atmosphere. Let us conceive of 
the atmosphere as made up of a great number of concen- 
tric strata, as AA, BB, CC, and DD, (Fig. 8,) increasing 
rapidly in density (as is known to be the fact) in ap- 
proaching near to the surface of the earth. Let S be a 
star, from" which a ray of Hght Sa enters the atmosphere 
at «, w^here, being much turned towards the radius of 
the convex surface,* it would change its direction into 
the line ab, and again into be, and cO, reaching the 
eye at O. Now, since an object alw^ays appears in the 
direction in which the light finally strikes the eye, the 
star w^ould be seen in the direction of the ray Oc, and 
therefore, the star would apparently change its place, 
in consequence of refraction, from S to S', being ele- 
vated out of its true position. Moreover, since on ac- 
count of the continual increase of density in descending 
through the atmosphere, the hght would be continually 
turned out of its course more and more, it w^ould there- 
fore move, not in the polygon represented in the figure, 
but in a corresponding curve, whose curvature is rapidly 
increased near the surface of the earth. 



68. What effect has refraction upon the place of a heavenly 
body? By what is it occasioned ? Illustrate by figure 8. How 
is a ray of light affected by passing out of a rarer into a denser 
medium? Why is an oar bent in the water ? In what line 
does the light move as it goes through the atmosphere ? 



* The operation of this principle is seen when an oar, or any stick, 
is thrust into water. As the rays of light by which the oar is seen, have 
their direction changed as they pass out of water into air, the apparent 
direction in which the body is seen is changed in the same degree, 
giving it a bent appearance. Thus, in the figure, if Sax represents- the 
oar, Sab will be the bent appearance as affected by refraction. The 
transparent substance through which any ray of light passes, is called 
a medium. It is a general fact in optics, that when light passes out of 
a rarer into a denser medium, as out of air into water, or out of space 
into air, it is turned tov^ards a perpendicular to the surface of the me- 
dium, and when it passes out of a denser into a rarer medium, as out 
of water into air, it is turned from the perpendicular. In the above 
ease the light, passing out of space into air, is turned towards the ra- 
dius of the earth, this being perpendicular to the surface of the atmos- 
phere; and it is turned more and more towards that radius the nearer 
it approaches to the earth, because the density of the air rapidly in- 
creases. 



40 



THE EARTH. 



69. When a body is in the zenith, since a ray of light 
from it enters the atmosphere at right angles to the re- 
fracting medium, it suffers no refraction. Consequently, 
the position of the heavenly bodies, when in the zenith, 
is not changed by refraction, while, near the horizon, 
where a ray of light strikes the medium very obliquely, 
and traverses the atmosphere through its densest part, 
the refraction is greatest. The following numbers, ta- 
ken at different altitudes, will show how rapidly refrac- 
tion diminishes from the horizon upwards. The amount 
of refraction at the horizon is 34' 00^'. At different ele- 
vations it is as follows : 



Elevation. 


Refraction. 


Elevation. 


Refraction. 


0° 10' 


82' 00" 


30° 


1' 40" 


0° 20' 


30' 00" 


40° 


r 09" 


1° 00' 


24' 25" 


45° 


0' 68" 


5° 00' 


10' 00" 


60° 


0' 33" 


10° 00' 


5' 20" 


80° 


0' 10" 


20° 00' 


2' 39" 


90° 


0' 00" 



From this table it appears, that while refraction at the 
horizon is 34 minutes, at so small an elevation as only 
10' above the horizon it loses 2 minutes, more than the 
entire change from the elevation of 30° to the zenith. 
From the horizon to 1° above, the refraction is dimin- 
ished nearly 10 minutes. The amount at the horizon, 
at 45°, and at 90*, respectively, is 34', 58", and 0. In 
finding the altitude of a heavenly body, the effect of pa- 
rallax must be added, but that of refraction subtracted. 

70, Since the whole amount of refraction near the 
horizon exceeds 33', and the diameters of the sun and 
moon are severally less than this, these luminaries are in 



69. Has refraction any effect on a body in the zenith ? Why 
not ? When is the refraction greatest ? What is the amount 
of refraction at the horizon ? How much does it lose within 
10' of the horizoQ ? What is the amomit of refraction at an 
elevation of 45^ ? 



REFRACTION. 41 

view both before they have actually risen and after they 
have set. 

The rapid increase of refraction near the horizon, is 
strikingly evinced by the oval figure which the sun as- 
sumes when near the horizon, and which is seen to the 
greatest advantage when light clouds enable us to view 
the solar disk. Were all parts of the sun equally raised 
by refraction, there would be no change of figure ; but 
since the low^er side is more refracted than the upper, 
the effect is to shorten the vertical diameter and thus to 
give the disk an oval form. This effect is particularly 
remarkable when the sun, at his rising or setting, is ob- 
served from the top of a mountain, or at an elevation 
near the sea shore ; for in such situations the rays of 
light make a greater angle than ordinary, wdth a perpen- 
dicular to the refracting medium, and the amount of re- 
fraction is proportionally greater. In some cases of this 
kind, the shortening of the vertical diameter of the sun 
has been observed to amount to &, or about one fifth of 
the whole. 

71. The apparent enlargemeint of the sun and moon 
in the horizon, arises from an optical illusion. These 
bodies in fact are not seen under so great an angle wdien 
in the horizon, as when on the meridian, for they are 
nearer to us in the latter case than in the former. The 
distance of the sun is indeed so great that it makes very 
little difference in his apparent diameter, w^hether he is 
viewed in the horizon or on the meridian ; but \\dth the 
moon the case is otherwise ; its angular diameter, w^hen 
measured w'ith instruments, is perceptibly larger at the 
time of its culmination. Why then do the sun and 
moon appear so much larger when near the horizon? It 



70. What effect has refraction upon the appearances of the 
sun and moon when near rising or setting? Explain the oval 
figure of the sun when near the horizon. In what position of 
the spectator does this phenomenon appear most conspicuous? 
How much has the vertical diameter of the sun ever appeared 
to t e shortened ? 

4* 



42 THE EARTH. 

is owing to that general law, explained in optics, by 
which we judge of the magnitudes of distant objects, 
not merely by the angle they subtend at the eye, but 
also by our impressions respecting their distance, allow- 
ing, under a given angle, a greater magnitude as we im- 
agine the distance of a body to be greater. Now, on ac- 
count of the numerous objects usually in sight between 
us and the sun, when on the horizon, he appears much 
farther removed from us than when on the meridian, and 
Te assign to him a proportionally greater magnitude. If 
we view the sun, in the two positions, through smoked 
glass, no such difference of size is observed, for here no 
objects are seen but the sun himself. 

The extraordinary enlargement of the sun or moon, 
particularly the latter, when seen at its rising through a 
grove of trees, depends on a different principle. Through 
the various openings between the trees, we see differ- 
ent images of the sun or moon, a great number of which 
overlapping each other, swell the dimensions of the 
body under the most favourable circumstances, to a very 
unusual size. 

TWILIGHT. 

72. Twilight also is another phenomenon depending 
upon the agency of the earth's atmosphere. It is that 
illumination of the sky which takes place just before 
sunrise, and which continues after sunset. It is due 
partly to refraction and partly to reflexion, but mostly to 
the latter. While the sun is within 18^ of the horizon, 
before it rises or after it sets, some portion of its light is 
conveyed to us by means of numerous reflections from 



71. To what is the apparent enlargement of the sun and 
moon when near the horizon owing ? Are these bodies seen 
under a greater angle when in the horizon than in the zenith ? 
To what general law of optics is the enlargement to be ascri- 
bed ? How is it when we view the sun through smoked glass ? 
To what is the extraordinary enlargement of these luminaries 
owing, when seen through a grove of trees ? 




the atmosphere. Let AB (Fig. 9.) be the horizon of 
the spectator at A, and let SS be a ray of Kght from the 
sun when it is two or three degrees below the horizon. 
Then to the observer at A, the segment of the atmos- 
phere ABS would be illuminated. To a spectator at C, 
whose horizon was CD, the small segment SJ)x would 
be the twilight ; while, at E, the twilight would disap- 
pear altogether. 

73. At the equator, where the circles of daily motion 
are perpendicular to the horizon, the sun descends 
through 18° in an hour and twelve minutes (T|-=l^h.), 
and the light of day therefore declines rapidly, and as 
rapidly advances after day break in the morning. At the 
pole, a constant twilight is enjoyed while the sun is 
within 18° of the horizon, occupying nearly two-thirds 
of the half year when the direct light of the sun is with- 
drawn, so that the progress from continual day to con- 



72. Define twilight — How many degrees below the horizon 
is the sun when it begins and ends 1 How is the light of the 
sun conveyed to us ? Explain by the iigiu'e. 

73. What is the length of twilight at the equator ? How 
long does it last at the poles ? How is the progress from con- 
tinual day to constant night? To the inhabitants of an oblique 
sphere, in what latitudes is twilight longest ? 



44 THE EARTH. 

stant night is exceedingly gradual. To the inhabitants 
of an oblique sphere, the twilight is longer in proportion 
as the place is nearer the elevated pole. 

74. Were it not for the power the atmosphere has of 
dispersing the solar light, and scattering it in various di- 
rections, no objects would be visible to us out of direct 
sunshine ; every shadow of a passing cloud would be 
pitchy darkness ; the stars w^ould be visible all day, and 
every apartment into w hich the sun had not direct ad- 
mission, would be involved in the obscui'ity of night. 
This scattering action of the atmosphere on the solar 
light, is greatly increased by the irregularity of tempera- 
ture caused by the sun, which throws the atmosphere 
into a constant state of undulation, and by thus bringing 
together masses of air of different temperatures, produces 
partial reflections and refractions at their common boun- 
daries, by w^hich means much light is turned aside from 
the direct course, and diverted to the purposes of general 
illumination. In the upper regions of the atmosphere, 
as on the tops of very high mountains, where the air is 
too much rarefied to reflect much light, the sky assumes 
a black appearance, and stars become visible in the day 
time. 



CHAPTER IV. 

OF TIME. 



75. Time is a measured 'portion of indefinite duration *^ 

The great standard of time is the period of the revo^ 

lution of the earth on its axis, which, by the most exact 



74. What would happen were it not for the power the at- 
mosphere has of dispersing the solar light ? What would every 
shadow of a cloud produce ? How is the scattering action of 
the atmosphere increased ? What is the aspect of the sky in 
the upper regions of the atmosphere ? 

* From old Eternity's mysterious orb, 

Was Time cut off and cast beneath the skies. — Young. 



TIME. 45 

observations, is found to be always the same. The time 
of the earth's revolution on its axis is called a sidereal 
day^ and is determined by the revolution of a star from 
the instant it crosses the meridian, until it comes round 
to the meridian again. This interval being called a si- 
dereal day, it is divided into 24 sidereal hours. Obser- 
vations taken upon numerous stars, in different ages of 
the world, show that they all perform their diurnal rev- 
olutions in the same time, and that their motion during 
any part of the revolution is perfectly uniform. 

76. Solar time is reckoned by the apparent revolution 
of the sun, from the meridian round to the same meridian 
again. Were the sun stationary in the heavens, like a 
fixed star, the time of its apparent revolution would be 
equal to the revolution of the earth on its axis, and the 
solar and the sidereal days would be equal. But since 
the sun passes from west to east, through 360° in 3651 
days, it moves eastward nearly 1° a day, (59' 8'^.3). 
While, therefore, the earth is turning round on its axis, 
the sun is moving in the same direction, so that when 
we have come round under the same celestial meridian 
from which we started, we do not find the sun there, 
but he has moved eastward nearly a degree, and the 
earth must perform so much more than one complete 
revolution, in order to come under the sun again. Now 
since a place on the earth gains 359° in 24 hours, how 
long will it take to gain 1° ? 
24 
359 : 24 : : 1 : 3^9=4^ nearly. 



75. Define time — What is the standard of time ? What is 
a sidereal day ? Do the stars all perform their revolutions in 
the same time ? Is their motion uniform ? 

76. How is the solar time reckoned? How far does the sun 
move eastward in a day ? How much longer is the solar than the 
sidereal day ? If we reckoned the sidereal day 24 hours, how 
should we reckon the solar ? Reckoning the solar day at 24 
hours, how long is the sidereal ? 



46 THE EARTH. 

Hence the solar day is about 4 minutes longer than 
the sidereal ; and if we were to reckon the sidereal day 
24 hours, we should reckon the solar day 24h. 4m. To 
suit the purposes of society at large, however, it is found 
most convenient to reckon the solar day 24 hours, and to 
throw the fraction into the sidereal day. Then, 

24h. 4m. : 24 : : 24 : 23h. 56m. nearly (23h. 56"^ 4^09) 
—the length of a sidereal day. 

77. The solar days, however, do not always differ from 
the sidereal by precisely the same fraction, since the in- 
crements of right ascension, which measure the differ- 
ence between a sidereal and a solar day, are not equal to 
each other. Apparent time, is time reckoned by the 
revolutions of the sun from the meridian to the meridian 
again. These intervals being unequal, of course the 
apparent solar days are unequal to each other. 

78. Mean time, is time reckoned by the average 
length of all the solar days throughout the year. This 
is the period which constitutes the civil day of 24 hours, 
beginning when the sun is on the lower meridian, name- 
ly, at 12 o'clock at night, and counted by 12 hours from 
the lower to the upper culmination, and from the upper 
to the lower. The astronomical day is the apparent so- 
lar day counted through the whole 24 hours, instead of 
by periods of 12 hours each, and begins at noon. Thus 

10 days and 14 hours of astronomical time, would be 

1 1 days and 2 hours of apparent time ; for when the 10th 
astronomical day begins, it is 10 days and 12 hours of 
civil time. 

79. Clocks are usually regulated so as to indicate mean 
solar time ; yet as this is an artificial period, not marked 



77. Do the solar days always differ from the sidereal by the 
same quantity ? Define apparent time. 

78. Define mean time. What constitutes the civil day ? 
What makes an astronomical day ? When does the civil day 
begin ? When does the astronomical day begin ? 



THE CALENDAR. 47 

off, like the sidereal day, by any natural event, it is ne- 
cessary to know how much is to be added to or sub- 
tracted from the apparent solar time, in order to give the 
corresponding mean time. The interval by which ap- 
parent time differs from mean time, is called the equation 
of time. If a clock were constructed (as it may be) so 
as to keep exactly with the sun, going faster or slower 
according as the increments of right ascension were 
greater or smaller, and another clock were regulated to 
mean time, then the difference of the two clocks, at any 
period, would be the equation of time for that moment. 
If the apparent clock were faster than the mean, then 
the equation of time must be subtracted ; but if the ap- 
parent clock were slower than the mean, then the equa- 
tion of time must be added, to give the mean time. 
The two clocks would differ most about the 3d of No- 
vember, when the apparent time is 16^^ greater than the 
mean (16™ 16^7). But, since apparent time is some- 
times greater and sometimes less than mean time, the 
two must obviously be sometimes equal to each other. 
This is in fact the case four times a year, namely, April 
15th, June 15th, September 1st, and December 24th. 

THE CALENDAR. 

80. The astronomical year is the time in which the 
sun makes one revolution in the ecliptic, and consists of 
365d. 5h. 48m. 51^-60. The civil year consists of 365 
days. The difference is nearly 6^ hours, making one day 
in four years. 

The most ancient nations determined the number of 
days in the year by means of the stylus, a perpendicular 



79. What time do clocks commonly keep 1 Define the equa- 
tion of time. How might two clocks be regulated so that their 
difference would indicate the equation of time 1 How must 
the equation of time be applied when the apparent clock is 
faster than the mean ? How when it is slower 1 When would 
the two clocks differ most 1 How much would they then differ? 
When would they come together ? 



48 THE EARTH. 

rod which casts its shadow on a smooth plane, bearing a 
meridian Hne. The time when the shadow was shortest, 
would indicate the day of the summer solstice ; and the 
number of days which elapsed until the shadow returned 
to the same length again, would show the number of 
days in the year. This was found to be 365 whole 
days, and accordingly this period w^as adopted for the 
civil year. Such a difference, however, betw^een the 
civil and astronomical years, at length threw all dates 
into confusion. For, if at first the summer solstice hap- 
pened on the 21st of June, at the end of four years, the 
sun would not have reached the solstice until the 22d of 
June, that is, it would have been behind its time. At 
the end of the next four years the solstice would fall on 
the 23d ; and in process of time it would fall succes- 
sively on every day of the year. The same would be 
true of any other fixed date. Julius Caesar made the 
first correction of the calendai', by introducing an inter- 
calary day every fourth year, making February to con- 
sist of 29 instead of 28 days, and of course the whole 
year to consist of 366 days. This fourth year was de- 
nominated Bissextile. It is also called Leap Year. 

81. But the true correction was not 6 hours, but 5h. 
49m. ; hence the intercalation was too great by 11 min- 
utes. This small fraction w^ould amount in 100 years 
to f of a day, and in 1000 years to more than 7 days. 
From the year 325 to 1582, it had in fact amounted to 
about 10 days ; for it was known that in 325, the vernal 
equinox fell on the 21st of March, whereas, in 1582 it 
fell on the 11th. In order to restore the equinox to the 
same date. Pope Gregory XIII, decreed, that the year 



80. Define the astronomical year — What is its exact period? 
Of how many days does the civil year consist? How much 
shorteris the civil than the astronomical year ? Howdidthemost 
ancient nations determine the number of days in the year ? 
When would the stylus mark the shortest day and when the 
longest T Explain the confusion which arose by reckoning the 
year only 365 days. How did Julius Csesar reform the calendar ? 



THE CALENDAR 49 

should be brought forward 10 days, by reckoning the 
5th of October the 15th. In order to prevent the cal- 
endar from falling into confusion afterwards, the follow- 
ing rule was adopted : 

Every year whose number h not divisible by 4 with- 
out a remainder, consists of 365 days ; every year which 
is so divisible, but is not divisible by 100, of 366; every 
year divisible by 100 but not by 400, again of 365 ; and 
every year divisible by 400, of 366. 

Thus the year 1838, not being divisible by 4, contains 
365 days, while 1836 and 1840 are leap years. Yet to 
make every fourth year consist of 366 days would in- 
crease it too much by about | of a day in 100 years; 
therefore every hundredth year has only 365 days. 
Thus 1800, although divisible by 4 was not a leap year, 
but a common year. But we have allowed a whole day 
in a hundred years, whereas we ought to have allowed 
only three fourths of a day. Hence, in 400 years we 
should allow a day too much, and therefore we let the 
400th year remain a leap year. This rule involves an 
error of less than a day in 4237 years. If the rule were 
extended by making every year divisible by 4000 (which 
would now^ consist of 366 days) to consist of 365 days, 
the error would not be more than one day in 100,000 
years. 

82. This reformation of the calendar was not adopted 
in England until 1752, by which time the error in the 
Julian calendar amounted to about 1 1 days. The year 
was brought forward, by reckoning the 3d of September 
the 14th. Previous to that time the year began the 25th 



81. By how many minutes was the allowance made by the 
Julian calendar too great ? To how much would the error 
amount in one hundred years ? To how much in a thousand 
years 1 To how much had it amounted from the year 325 to 
1582 ■? What changes did Pope Gregory make in the year? 
State the rule for the calendar. Of the three years 1836, 
1838, and 1840, which are leap years ? Was 1800 aleap year? 
How is every 400th year ? 

5 



50 THE EARTH. 

of March ; but it was now made to begin on the 1st of 
January, thus shortening the preceding year, 1751, one 
quarter.* 

As in the year 1582, the error in the JuHan calendar 
amounted to 10 days, and increased by f of a day in a 
century, at preseK»t the correction is 12 days ; and the 
number of the year will differ by one with respect to 
dates between the 1st of January and the 25th of March. 

Examples. General Washington was born Feb. 11, 
1731, old style ; to what date does this correspond in 
new style ? 

As the date is the earlier part of the 18th century, the 
correction is 1 1 days, which makes the birth day fall on 
the 22d of February ; and since the year 1731 closed 
the 25th of March, w^iile according to new style 1732 
would have commenced on the preceding 1st of Janu- 
ary ; therefore, the time required is Feb. 22, 1732. It 
is usual, in such cases, to write both years, thus : Feb. 
11, 1731-2, O. S. 

2. A great eclipse of the sun happened May 15th, 
1836 ; to what date would this time correspond in old 
style 1 Ans. May 3d. 

83. The common year begins and ends on the same 
day of the week ; hut leap year ends one day later in the 
week than it began. 

For 52x7 = 364 days ; if therefore the year begins 
on Tuesday, for example, 364 days would complete 52 
weeks, and one day would be left to begin another week, 



82. When was this reformation first adopted in England ? 
How was the year brought forward ? When did the year be- 
gin before that time ? To how many days did the error amount 
in 1752 ? How many days are allowed at present between 
old and new style ' 



* Russia, and the Greek Church generally, adhere to the old style. 
In order to make the Russian dates correspond to ours, we must add to 
them 12 days. France and other Catholic countries, adopted the G'e- 
gorian calendar soon after it was promulgated 



ASTRONOMICAL INSTRUMENTS. 51 

and the following year would begin on Wednesday. 
Hence, any day of the month is one day later in the 
week than the corresponding day of the preceding year. 
Thus, if the 16th of November, 1838, falls on Friday, 
the 16th of November, 1837, fell on Thursday, and in 
1839 will fall on Saturday. But if leap year begins on 
Sunday, it ends on Monday, and the following year be- 
gins on Tuesday ; while any given day of the month is 
two days latei in the week than the corresponding date 
of the preceding year. 



CHAPTER V. 

OF ASTRONOMICAL LNSTRUMENTS FIGURE AND DENSITY OP 

THE EARTH. 

84. The most ancient astronomers employed no in- 
struments of observation, but acquired their knowledge 
of the heavenly bodies by long continued and most at- 
tentive inspection with the naked eye. Instruments for 
measuring angles were first used in the Alexandrian 
school, about 300 years before the Christian era. 

85. Wherever we are situated on the earth we appear 
to be in the center of a vast sphere, on the concave sur- 
face of which all celestial objects are inscribed. If we 
take any two points on the surface of the sphere, as two 
stars for example, and imagine straight lines to be drawn 
to them from the eye, the angle included between these 



83. If the common year begins on a certain day of the week, 
how will it end ? How is it with leap year ? How does any 
day of the month compare in the preceding and following yeai 
with respect to the day of the week ? How is this in leap 
year ? 

84. How did the most ancient nations acquire their knowl- 
edge of the heavenly bodies ? When were astronomical in- 
struments first introduced ? 



52 THE EARTH. 

lines will be measured by the arc of the sky contained 
between the two points. Thus if HBD, (Fig. 10,) rep- 
Fig. 10. 




resents the concave surface of the sphere, A, B, two 
points on it, as two stars, and CA, CB, straight lines 
drawn from the spectator to those points, then the angu- 
lar distance between them is measured by the arc AB, 
or the angle ACB. But this angle may be measured on 
a much smaller circle, having the same center, as EFG, 
since the arc EF will have the same number of degrees 
as the arc AB. The simplest mode of taking an angle 
between two stars, is by means of an arm opening at a 
joint Hke the blade of a penknife, the end of the arm 
moving like CE upon the graduated circle KEG. 

The common surveyor's compass affords a simple ex- 
ample of angular measurement. Here the needle lies in 
a north and south line, while the circular rim of the 
compass, when the instrument is level, corresponds to 
the horizon. Hence the compass shows how many de- 
grees any object to which we direct the eye, lies east or 
west of the meridian. 



85. How is the angular distance between two points on the 
celestial sphere measured ? Explain figure 10, Show how the 
circles of the sphere may be truly represented by the smaller 
circles of the instrument, as the horizon by the surveyor's com- 
pass. Explain the simplest mode of taking angles by figure 10. 



ASTRONOMICAL INSTRUMENTS. 53 

86. It is obvious that the larger the graduated circle 
is, the more minutely its limb may be divided. If the 
circle is one foot in diameter, each degree will occupy 
jij of an inch. If the circle is 20 feet in diameter, a 
degree will occupy the space of two inches and could 
be easily divided to minutes, since each minute would 
cover a space of -^ of an inch. Refined astronomical 
circles are now divided with very great skill and accu- 
racy, the spaces between the divisions being, when read 
off. magnified by a microscope ; but in former times, 
astronom-ers had no mode of measuring small angles 
but by employing very large circles. But the telescope 
and microscope enable us at present to measure celestial 
arcs m.uch more accurately than was done by the older 
astronomers. 

The principal instruments employed in astronomy, 
are the Telescope, the Transit Instrument, the Altitude 
and Azimuth Instrument, and the Sextant. 

87. The Telescope has greatly enlarged our knowl- 
edge of astronomy, both by revealing to us many things 
invisible to the naked eye, and also by enabling us to 
attain a much higher degree of accuracy than we could 
otherwise reach, in angular measurements. It was in- 
vented by Galileo about the year 1600. The powers of 
the telescope were improved and enlarged by successive 
efforts, and finally, about 50 years ago, telescopes were 
constructed in England by Dr. Herschel, of a size and 
power that have not since been surpassed. 

A complete knovrledge of the telescope cannot be ac- 
quired without an acquaintance with the science of op- 
tics ; but we may perhaps convey to one unacquainted 
with that science, some idea of the leading principles of 



86. What is the advantage of having large circles for angu- 
lar measurements 1 When the circle is one foot in diameter, 
what space will 1° occupy on the limb ? What space when 
the circle is twenty feet in diameter ? What are the princi- 
pal instruments used in astronomical observations 1 



54 



THE EARTH. 



this noble instrument. By means of the telescope, we 
first form an image of a distant object as the moon for 
example, and then magnify that image by a microscope. 
Let us first see how the 'image is formed. This may be 
done either by a convex lens, or by a concave mirror. A 
convex lens is a flat piece of glass, having its two faces 
convex, or spherical, as is seen in a common sun glass. 
Every one who has seen a sun glass, knows that when 
held towards the sun it collects the solar rays into a 
small bright circle in the focus. This is in fact a small 
image of the sun. In the same manner the image of 
any distant object, as a star, may be formed as is repre- 
sented in the following diagram. Let ABCD represent 
Fig. 11. 




the tube of a telescope. At the front end, or at the end 
which is directed towards the object, (which we will 
suppose to be the moon,) is inserted a convex lens, 
L, which receives the rays of light from the moon, and 
collects them into the focus at a, forming an image of 
the moon. This image is viewed by a magnifier attach- 
ed to the end BC. The lens L is called the object-glass, 
and the microscope in BC the eye-glass. We apply a 
magnifier to this image just as we would to any object ; 



87. Who invented the telescope ? Who constructed tele- 
scopes of great size and power ? Explain the leading prin- 
ciple of the telescope. How is the image formed ? What is 
a convex lens ? How does it affect parallel rays of light ? 
How do we view the image formed by the lens ? How is the 
image magnified 1 How is it rendered brighter ? 



ASTRONOMICAL INSTRUMENTS. 55 

and by greatly enlarging its dimensions, we may render 
its various parts far more distinct than they would other- 
wise be, while at the same time the object lens collects 
and conveys to the eye a much greater quantity of light 
than would proceed directly from the body under exam- 
ination. A very small beam of light only from a distant 
object, as a star, can enter the eye directly ; but a lens 
one foot in diameter will collect a beam of light of the 
same dimensions, and convey it. to the eye. By these 
means many obscure celestial objects become distinctly 
visible, which would otherwise be either too minute, or 
not sufficiently luminous to be seen by us. 

88. But the image may also be formed by means of a 
concave mirror, which, as well as the convex lens, has 
the property of collecting the rays of light which pro- 
ceed from any luminous body, and of forming an image 
of that body. The image formed by the concave mir- 
ror is magnified by a microscope in the same manner as 
when formed by the convex lens. When the lens is 
used to form an image, the instrument is called a Re- 
fracting telescope ; when a concave mirror is used, it is 
called a P^efiecting telescope. 

The telescope in its simples-t form is employed not so 
much for angular measurements, as for aiding the pow- 
ers of vision in viewing the celestial bodies. When di- 
rected to the sun, it reveals to us various irregularities on 
his disk not discernible by naked vision ; w^hen turned 
upon the moon or the planets, it affords us new and in- 
teresting views, and enables us to see in them the linea- 
ments of other worlds ; and when brought to bear upon 
the fixed stars, it vastly increases their number and re- 
veals to us many surprising facts respecting them. 



88. How is an image formed by a concave mirror? How is 
this image magnified ? When is the instrument called a re- 
fracting and when a reflecting telescope ? For what pur- 
poses are telescopes chiefly employed ? 



56 



THE EARTH. 



89. Tlie Transit Instrument is a telescope, which is 
fixed permanently in the meridian, and moves only in 
that plane. It rests on a horizontal axis, which consists 
of two hollow cones applied base to base, a form uniting 
lightness and strength. The two ends of the axis rest 
Fig. 12. 




on two firm supports, as pillars of stone, for example, so 
connected with the building as to be as free as possible 
from all agitation. In figure 12, AD represents the tele- 



89. What is a Transit Instrument ? On what supports does 
it rest as represented in figure 12. Why are they made so firm? 
Describe all parts of the instrument. What is its use ? How 
used to regulate clocks and watches ? What kind of time is 
shown when the sun is on the meridian ? How is this con- 
verted into mean tme ? Give an example. 



ASTRONOMICAL INSTRUMENTS. 57 

scope, E, W, massive stone pillars supporting the hori- 
zontal axis, beneath which is seen a spirit level, (which 
is used to bring the axis to a horizontal position,) and n 
a vertical circle graduated into degrees and minutes. 
This circle serves the purpose of placing the instrument 
at any required altitude, or distance from the zenith, and 
of course for determining altitudes and zenith distances. 
The use of the transit instrument is to show the pre- 
cise moment when a heavenly body is on the meridian. 
One of its uses is to enable us to obtain the true time, 
and thus to regulate our clocks and watches. We find 
w^hen the sun's center is on the meridian, and this gives 
us the time of noon or apparent time. (Art. 78.) But 
watches and clocks usually keep mean time, and there- 
fore in order to set our time piece by the transit instru- 
ment, we must apply the equation of time. 

90. A noon mark may easily be made by the aid of 
the Transit Instrument. A window sill is frequently 
selected as a suitable place for the mark, advantage be- 
ing taken of the shadow projected upon it by the per- 
pendicular casing of the window. Let an assistant stand 
with a rule laid on the line of shadow and with a knife 
ready to make the mark, the instant when the observer 
at the Transit Instrument announces that the center of 
the sun is on the meridian. By a concerted signal, as 
the stroke of a bell, the inhabitants of a town may all 
fix a noon mark from the same observation. It must be 
borne in mind, however, that the noon mark gives the 
apparent time, and that the equation of time must be 
allowed for in setting the clock or watch. Suppose w^e 
wish to set our clock right on the first of January. We 
find by a table of the equation of time, that mean time 
then precedes apparent time 3m. 43s. ; we must there- 
fore set the clock at 3m. 43s. the instant the center of 
the sun is on the meridian. If the time had been the 
first of May instead of the first of January, then we 
find by the table that 3m. is to be subtracted from the 
apparent time, and consequently, w^hen the center of the 

90 Describe the mode of making a noon mark. 



58 



THE EARTH. 



sun was on the meridian, we should set our clock at llh. 
57m. or 3m. before twelve. 

91. The equation of time varies a little with different 
years, but the following table will always be found 
within a few seconds of the truth. The equation for 
the current year is given exactly in the American Al- 
manac. 





Equation of Time j 


or Apparent Noon. 




. 


Jan. 1 Feb. 


xMAR.IArR. 


May 


JUN. 


JOL. 


Aug 


Sept. 


Oct. Nov. 


D 1 


>> 


Add. 1 Add. 


Add. 


Add. 


Sub. 


Sub. 


Add. 


Add. 


Add. 


Sub. Sub. 


Sub. 


Q_ 








.M. S. 










M. S. M. 3. 




3.43 13.53 


12.42 


4T6 


370 


2.38 


3.19 


673 


ai). 1 


10. 916.15 


10.54 


9, 


4.1114. 1 


12.30 


3.48 


3. 7 


2.29 


3.31 


5.59 


50.17 


10.2816.16 


10.32 


?. 


4.3914. 8 


12.18 


3.30 


3.15 


2.19 


3.4215 55 


0.36 


10.4716.17 


10. 8 


4 


5. 714.14 12. 5 


3.12 


3.21 


2.10 


3.535.50 


0.56 


11. 616.17 


9.45 


5 


5.3414.19111.51 

6. 114.24111.38 


2.54 
2.37 


3.27 
3.32 


2. 
1.49 


4. 4,5.45 


1.15 


11.2116.16 
11.4216.14 


9.20 

8.55 


4.15 5.39 


1.35 


7 


6.27 14.27! 11.23 


2.19 


3.37 


1.39 


4.25;5.33 


1.55 


11.59 16.11 


8.30 


8 


6.5314.30;U. 8 


2. 2 


3.42 


1.28 


4.34 5.25 


2.15 


12.1616. 7 


8. 4 


9 


7.1&14.32{10.53 


1.45 


3.46 


1.17 


4.44 5.18 


2.36 


12.3316. 3 


7.37 


10 
11 


7.4314.33 10.38 


1.28 


3.49 


1. 5 


4.53 5. 9 


2.56 


12.4945.58 


7.10 


8. 7114.34:10.22 


l.il 


3.51 


0.53 


5. 15. 1 


3.17 


13. 5115.51 


6.43 


12 


8.31 14.33:10. 6 


0.55 


3.53 


0.41 


5. 9 4.51 


3.38 


13.20:15.41 


6.15 


13 


8.54114.32 


9.49 


0.39 


3.55 


0.29 


5.174.41 


3.59 


I3.34ll5.37 


5.47 


14 


9.1614.30 


9.32 


0.23 


3.56 


0.17 


5.24 4.31 


4.20 


13.49 15.28 


5.18 


15 


9.37; 14.28 


9.15 


0. 8 


3.56 


0. 4 


5.30 4.20 


4.41 


14. 215.18 


4.49 


1 




Sub. 




Add. 






i 




16 


9.5814.25 


8.5ft 


0. 7 


3.56 


0. 8 


5.37 4. 8 


5. 2 


14.15 15. ft 


4.20 


17 


10.1914.20 


8.41 


0.22 


3.55 


0.21 


5.42J3.56 


5.23 


14,28 14.56 


3.50 


18 


10.38,14.16 


8.23 


0.36 


3.54 


0.34 


5.483.44 


5.44 


14.39 14.44 


3.21 


19 


10.5714.10 


8. ^ 


0.50 


3.52 


0.47 


5.52:3.31 


6. 5 


14.51 14.31 


2.51 


20 
21 


11.1514. 4 


lAl 


1. 3 
1.16 


3.49 
3.46 


I. 
1.13 


5.5713.17 
6. 013. 3 


6.26 
6.47 


15. 1 14.17 
15.11 il4. 3 


2.21 
1.51 


11.3313.58 


7.29 


22 


11.4913.50 


7.11 


1.29 


3.42 


1.26 


6. 32.49 


7. 8 


15.2113.47 


1.21 


23 


12. 513.42 


6.52 


1.41 


3.38 


1.39 


6. 62.34 


7.29 15.29 13.31 


0.51 


24 


12.2013.34 


6.34 


1.52 


3.33 


1.52 


6. 82.19 


7.4915 3713.14 


0.21 


25 


12.3513.25 


6.15 


2. 4 


3.28 


2.5 


6. 9I2. 3 


8 1015.44 12.56'«0. 9| 


26 


12.4813.15 


5..n7 


2.14 


3.22 


2.18 


610:1.47 


8.3oil5.5l 12.38 


0.39 


27 


13. 1 13. 4 


5.38 


2.24 


3.16 


2.30 


6.104.30 


8.50jl5..57 12.18 


1. 9 


28 


13.1312.54 


5.20 


2.34 


3. 9 2.43 


6.10I1.13 


9.1l!l6. 2 11.58 


1.39 


29 


13.24 


5. 1 


2.43 


3. 2 


2.55 


6. 9;0.56 


9.30J10. 611.38 


2. 8 


31 


13.35 
13.44 


4.43 
4.25 


2.52 


2 54 


3. 8 


6. 80.38 


9.50il6.10 11.16 


2.37 




2.46 




6. 5!o.20 


Il6.13| 


3. 6 



91. Is the equation of time the same or different in different 
years ? In what book may it be found exactly for the cur- 
rent year ? 



ASTRONOMICAL INSTRUMENTS. 59 

92. The Astronomical Clock is the constant compan- 
ion of the Transit Instrument. This clock is so regu- 
lated as to keep exact pace with the stars, and of course 
with the revolution of the earth on its axis ; that is, it 
is regulated to sidereal time. It measures the progress 
of a star, indicating an hour for every 15°, and 24 hours 
for the whole period of the revolution of the star. Si- 
dereal time, it will be recollected, commences when the 
vernal equinox is on the meridian, just as solar time com- 
mences when the sun is on the meridian. Hence, the 
hour by the sidereal clock has no correspondence with 
the hour of the day, but simply indicates how long it is 
since the equinoctial point crossed the meridian. For 
example, the clock of an observatory points to 3h 20m. ; 
this may be in the morning, at noon, or any other time 
of the day, since it merely shows that it is 3h. 20m. 
since the equinox was on the meridian. Hence, when 
a star is on the meridian, the clock itself shows its right 
ascension ; (Art. 24,) and the interval of time between 
the arrival of any two stars upon the meridian, is the 
measure of their difference of right ascension. 

93. Astronomical clocks are made of the best work- 
manship, with a compensation pendulum, and every 
other advantage which can promote their regularity. 
The Transit Instrument itself, when once accurately 
placed in the meridian, affords the means of testing the 
correctness of the clock, since one revolution of a star 
from the meridian to the meridian again, ought to cor- 
respond to exactlv 24 hours by the clock, and to con- 



92. How is the astronomical clock regulated 1 What does 
it measure ? How many degrees does a star pass over in an 
hour? When does sidereal time commence ? W^hat is de- 
noted by the hour and minute of a sidereal clock ? How do 
we determine the right ascension of a star \ 

93. How is the Avorkmanship of astronomical clocks ? How 
is the correctness of a clock tested ? To what degree o^ 
perfection are clocks brought? By what instrument are 
clocks re collated'? 



60 THE EARTH. 

tinue the same from day to day ; and the right ascen- 
sion of various stars as they cross the meridian, ought 
to be such by the clock as they are given in the tables, 
where they are stated according to the accurate determi- 
nations of astronomers. Or by taking the difference of 
right ascension of any tv^o stars on successive days, it 
will be seen whether the going of the clock is uniform 
for that part of the day ; and by taking the right ascen- 
sion of different pairs of stars, we may learn the rate of 
the clock at various parts of the day. We thus learn, 
not only whether the clock accurately measures the 
length of the sidereal day, but also whether it goes uni- 
formly from hour to hour. 

Although astronomical clocks have been brought to a 
great degree of perfection, so as to vary hardly a second 
for many months, yet none are absolutely perfect, and 
most are so far from it as to require to be corrected by 
means of the Transit Instrument every few days. In- 
deed, for the nicest observations, it is usual not to at- 
tempt to bring the clock to an absolute state of correct- 
ness, but after bringing it as near to such a state as can 
conveniently be done, to ascertain how much it gains 6r 
loses in a day ; that is, to ascertain its rate of going, and 
to make allowance accordingly. 

94. The Transit Instrument is adapted to taking obser- 
vations on the meridian only ; but we sometimes require 
to know the altitude of a celestial body when it is not 
on the meridian, and its azimuth, or distance from the 
meridian measured on the horizon. An instrument es- 
pecially designed to measure altitudes and azimuths, is 
called an Altitude and Azimuth Instrument, whatever 
may be its particular form. \V hen a point is on the hor- 
izon its distance from the meridian, or its azimuth, may 
be taken by the common surveyor's compass, the direc- 



94. To what kind of observations only is the transit mslru- 
ment adapted ? What instrument is employed for finding alti- 
tude and azimuth ? Describe the Altitude and Azirauth In- 
strument from figure 13 



ASTRONOMICAL INSTRU5IENTS. 



61 



tion of the meridian being determined by the needle ; 
but when the object, as a star, is not on the horizon, its 
azimuth, it must be remembered, is the arc of the hori- 
zon from the meridian to a vertical circle passing through 
the star ; at whatever diiierent altitudes, therefore, two 
stars may be, and however the plane which passes 
through them may be inclined to the horizon, still it is 
their angular distance measured on the horizon which 
determines their difference of azimuth. Figure 13 rep- 
resents an Altitude and Azimuth Instrument, several of 
the usual appendages and subordinate contrivances being 
omitted for the sake of distinctness and simplicity. Here 
abc is the vertical or altitude circle, and EFG the hori- 
zontal or azimuth circle ; AB is a telescope mounted on 
Fig. 13. 




a horizontal axis and capable of two motions, one in al- 
titude parallel to the circle ahc, and the other in azimuth 
parallel to EFG. Hence it can be easily brought to 



62 THE EARTH. 

bear upon any object. At m, under the eye glass of the 
telescope, is a small mirror placed at an angle of 45° 
with the axis of the telescope, by means of which the 
image of the object is reflected upw^ards, so as to be 
conveniently presented to the eye of the observer. At d 
is represented a tangent screw, by which a slow motion 
is given to the telescope at c. At h and g are seen two 
spirit levels, at right angles to each other, which show 
when the azimuth circle is truly horizontal. The in- 
strument is supported on a tripod, for the sake of greater 
steadiness, each foot being furnished with a screw for 
levelling. '\ .- 

95. The Sextant is an instrument used for taking the 
angular distance between any two bodies on the surface 
of the celestial sphere, by reflecting the image of one of 
the bodies so as to coincide with the other body as seen 
directly. It is particularly valuable for measuring celes- 
tial arcs at sea, because it is not, like most astronomical 
instruments, affected by the motion of the ship. 

Tliis instrument (Fig 14,) is of a triangular shape, 
and is made strong and firm by metallic crossbars. It 
has two reflectors, I and H, called, respectively, the Index 
Glass, and the Horizon Glass, both of which are firmly 
fixed perpendicular to the plane of the instrument. The 
Index Glass is attached to the movable arm ID and 
turns as this is moved along the graduated limb EF. 
This arm also carries a Vernier at D, which enables us to 
take oflf minute parts of the spaces into which the limb 
is divided. The Horizon Glass, H, consists of two 
parts ; the upper being transparent or open, so that the 
eye, looking through the telescope T, can see through 
it a distant body as a star at S, while the lower part is 
a reflector. 



95. Define the Sextant — For what is it particularly valu- 
able ? Describe it from figure 14. Where is the Vernier and 
what is its use ? Specify the manner in which the light comes 
from the object to the eye. How can we measure the angulai 
distance between the moon and a star ? 



ASTRONOMICAL INSTRUMENTS. 



63 



Suppose it were required to measure the angular dis- 
tance between the moon and a certain star, the moon 

Fig. 14. 




being at M, and the star at S. The instrument is held 
fii'mly in the hand, so that the eye, looking through the 
telescope, sees the star S through the transparent part of 
the Horizon Glass. Then the movable arm ID is moved 
from F towards E, until the image of M is carried down 
to S, when the number of degrees and parts of a degree 
reckoned on the limb from F to the index at D, will 
show the angular distance betw^een the two bodies. 

FIGURE AND DENSITY OF THE EARTH. 



96. We have already shown, that the figure of the 
earth is nearly globular ; but since the semi-diameter of 
the earth is taken as the base line in determining the 
parallax of the heavenly bodies, and lies therefore at the 
foundation of all astronomical measurements, it is very 



64 



THE EARTH. 



important that it should be ascertained with the greatest 
possible exactness. Having now learned the use of as- 
tronomical instruments, and the method of measuring 
arcs on the celestial sphere, we are prepared to under- 
stand the methods employed to determine the exact fig- 
ure of the earth. This element is indeed ascertained 
in different ways, each of which is independent of all 
the rest, namely, by investigating the effects of the cen- 
trifugal force arising from the revolution of the earth 
on its axis — by measuring aixs of the meridian — and by 
experiments with the pendulum. 

97. First, the known effects of the centrifugal force, 
would give to the earth a spheroidal figure, elevated in 
the equatorial, and flattened in the polar regions. 

By the centrifugal force is meant, the tendency which 
revolving bodies exhibit to recede from the 
center. Thus when a grindstone is turn- 
ed swiftly, water is thrown off from it in 
straight lines. The same effect is notic- 
ed w hen a carriage wheel is driven rapidly 
thi'ough the water. If a pail, containing 
a little water, is whirled, the water rises 
on the sides of the pail in consequence of 
the centrifugal force. The same principle 
is more strikingly illustrated by the annex- 
ed cut, (Fig. 15,) which represents an 
open glass vessel suspended by a cord at- 
tached to its opposite sides, and passed 
through a staple in the ceiling of the room. 
A little water is introduced into the ves- 
sel which is made to whirl rapidly by ap- 
plying the hand to the opposite sides. As 
it turns, the water rises on the sides of the 
vessel, receding as far as possible from the 




96. Why is it so necessary to ascertain accurately the semi- 
diameter of the earth ? In how many different ways is this 
element ascertained ? Specify them. What is iueant by the 
centrifugal force ? Give an illustration. Describe figure 1 5. 



ASTRONOMICAL INSTRUMENTS. 65 

center. The same effect is produced by suiFering the 
cord to untwist freely, which gives a swift revolution 
to the vessel. In like manner, a ball of soft clay when 
made to turn rapidly on its axis, sw^ells out in the central 
parts and becomes flattened at the ends, forming the fig- 
ure called an oblate spheroid. 

Had the earth been originally constituted (as geolo- 
gists suppose) of yielding materials, either fluid or semi- 
fluid, so that its particles could obey their mutual at- 
traction, w^hile the body remained at rest it would spon- 
taneously assume the figure of a perfect sphere ; as soon, 
however, as it began to revolve on its axis, the greater 
velocity of the equatorial regions would give to them a 
greater centrifugal force, and cause the body to swell 
out into the form of an oblate spheroid. Even had the 
solid part of the earth consisted of unyielding materials 
and been created a perfect sphere, still the waters that 
covered it would have receded from the polar and have 
been accumulated in the equatorial regions, leaving bare 
extensive regions on the one side, and ascending to a 
mountainous elevation on the other. 

On estimating, from the know^n dimensions of the 
earth and the velocity of its rotation, the amount of the 
centrifugal force in different latitudes, and the figure of 
equilibrium w^hich would result, Newton inferred that 
the earth must have the form of an oblate spheroid be- 
fore the fact had been established by observation ; and 
he assigned nearly the true ratio of the polar and equa- 
torial diameters. 



97. What would be the figure of the earth derived fi-oin the 
centrifugal force ? What figure would the earth have assumed 
if at rest 1 How would this figure be changed when it began to 
revolve ? Had the earth been originally a solid sphere covered 
with water, how would the water have disposed itself when the 
earth was made to turn on its axis ? How was the spheroidal 
figure of the earth inferred before the fact was established by 
observation 1 

6* 



66 



THE EARTH. 



98. Secondly, the, spheroidal figure of the earth is 
proved, by actually measuring the length of a degree on 
the meridian in different latitudes. 

Were the earth a perfect sphere, the section of it made 
by a plane passing through its center in any direction 
would be a perfect circle, whose curvature would be 
equal in all parts ; but if we find by actual observation, 
that the curvature of the section is not uniform, we in- 
fer a corresponding departure in the earth from the figure 
of a perfect sphere. The task of measuring portions of 
the meridian, has been executed in different countries. 
We may know, in each case, how far we advance on 
the meridian, because every step we take northward, 
produces a corresponding increase in the altitude of the 
north star. That an increase of the length of the de- 
grees of the meridian, as we advance from the equator 
towards the pole, really proves that the earth is flattened 
at the poles, will be readily seen on a little reflection. 
We must bear in mind that a degree is not any certain 
leiigth, but only the three hundred and sixtieth part of a 
circle, whether great or small. If, therefore, a degree is 
longer in one case than in another, we infer that it is the 
three hundred and sixtieth part of a larger circle ; and 
since we find that a degree towards the pole is longer 
than a degree towards the equator, we infer that the cur- 
vature is less in the former case than in the latter. 

The result of all the measurements is, that the length 
of a degree increases as we proceed from the equator 
towards the pole, as may be seen from the following 
table : 



98. By what measurements is the spheroidal figure of tho 
earth proved ? What would be the curvature in all parts were 
the earth a perfect sphere ? How may we know when we have 
advanced one degree northward in the meridian ? Explain how 
an increase of the length of a degree proves that the earth is 
flattened towards the poles ? In what places have arcs of the me- 
ridian been measured 1 What is the mean diameter of the 
earth ? What is the difference between the two diameters ? 
What fraction expresses the ellipticity of the earth ? 



ASTRONOMICAL IXSTRUMENTS. 



67 



Places of observation. 
Peru, 


Latitude. 


Length of a degree in miles 


00° 00' 00" 


68.732 


Pennsylvania, 


30 12 00 


68.896 


Italy, 


43 01 00 


68.998 


France, 


46 12 00 


69.054 


England, 


51 29 54i 


69.164 


Sweden, 


66 20 10 


69.292 



Combining the results of various estimates, the di- 
mensions of the terrestrial spheroid are found to be as 
follows : 

Equatorial diameter, . . . 7925.648 

Polar diameter, '. . . . 7899.170 
Mean diameter, .... 7912.409 

The difference between the greatest and the least, is 
26.478 = gig of the greatest. This fraction (^Jg) is de- 
nominated the ellipticity of the earth, being the excess 
of the longest over the shortest diameter. 

99. Thirdly, the figure of the earth is shown to be 
spheroidal, by observations with the pendulum. 

If a pendulum, like that of a clock, be suspended 
and the number of its vibrations per hour be counted, 
they will be found to be different in different latitudes. 
A pendulum that vibrates 3600 times per hour at the 
equator, will vibrate 3605f times at London, and a still 
greater number of times nearer the north pole. Now the 
vibrations of the pendulum are produced by the force of 



96. Explain -how we may ascertain the figure of the earth by 
means of a pendulum — How will the number of vibrations be 
in different latitudes ? How many times will a pendulum vi- 
brate in an hour at London, which vibrates 3600 times per hour 
at the equator ? How are the vibrations of the pendulum pro- 
duced 1 Why are these comparative numbers at different 
places measures of the relative distances from the center of the 
earth ? What could we infer from two observations with the 
pendulum, one at the equator and the other at the north pole ? 
To what conclusions have pendulum observations, made in va- 
rious parts of khe earth, led ? 



68 



THE EARTH. 



gravity. Hence their comparative number at different 
places is a measure of the relative forces of gravity at 
those places. But when we know the relative forces of 
gravity at different places, we know their relative dis- 
tances from the center of the earth, because the nearer a 
place is to the center of the earth, the greater is the force 
of gravity. Suppose, for example, we should count the 
number of vibrations of a pendulum at the equator, and 
then carry it to the north pole and count the number of 
vibrations made there in the same time ; we should be 
able from these two observations to estimate the relative 
forces of gravity at these two points ; and having the rel- 
ative forces of gravity, we can thence deduce their rela- 
tive distances from the center of the earth, and thus ob- 
tain the polar and equatorial diameters. Observations 
of this kind have been taken with the greatest accuracy 
in many places on the surface of the earth, at various 
distances from each other, and they lead to the same 
conclusions respecting the figure of the earth, as those 
derived from measuring arcs of the meridian. 

100. The density of the earth compared with w^atcr, 
that is, its specific gravity, is 5-Jo The density was first 
estimated by Dr. Hutton, from observations made by Dr. 
Maskeiyne, Astronomer Royal, on SchehalHen, a moun- 
tain of Scotland, in the year 1774. Thus, let M (Fig. 
16,) represent the mountain, D, B, two stations on o}> 
posite sides of the mountain, and I a star ; and let IE 
and IG be the zenith distances as determined by the 
difference of latitude of the two stations. But the ap- 
parent zenith distances as determined by the plumb line 
are IE' and IG'. The deviation towards the mountain 
on each side exceeded 7". The attraction of the moun- 
tain being observed on both sides of it, and its mass be- 
ing computed from a number of sections taken in all di- 



100 What is the specific gravity of the earth ? How was it 
ascertained? Explain figure 16. Why is the density of the 
earth so important an element ? 



DENSITY OF THE EARTH. 



69 




rections, tnese data, when compared with the known 
attraction and magnitude of the earth, led to a knowl- 
edge of its mean density. According to Dr. Hutton, 
this is to that of water as 9 to 2 ; but later and more ac- 
curate estimates have made the specific gravity of the 
earth as stated above. But this density is nearly double 
the average density of the materials that compose the 
exterior crust of the earth, showing a great increase of 
density towards the center. 

The density of the earth is an important element, as 
we shall find that it helps us to a knowledge of the den- 
sity of each of the other members of the solar system. 



PART II. OF THE SOLAR SYSTEM. 



101. Having considered the Earth, in its astronomical 
relations, and the Doctrine of the Sphere, we proceed 
now to a survey of the Solar System, and shall treat suc- 
cessively of the Sun, Moon, Planets, and Comets. 



CHAPTER I. 



OF THE SUN SOLAR SPOTS ZODIACAL LIGHT. 



102. Tub figure which the sun presents to us is that 
of a perfect circle, w^hereas most of the planets exhibit a 
disk more or less elliptical, indicating that the true shape 
of the body is an oblate spheroid. So great, however, 
is the distance of the sun, that a line 400 miles long 
would subtend an angle of only 1'^ at the eye, and would 
therefore be the least space that could be measured. 
Hence, were the difference between two conjugate di- 
ameters of the sun any quantity less than this, we could 
not determine by actual measurement that it existed at 
all. Still we learn from theoretical considerations, 
founded upon the known effects of centrifugal force, 
arismg from the sun's revolution on his axis, that his 
figure is not a perfect sphere, but is slightly spheroidal. 

103. The distance of the sun from the earth, is nearly 
95,000,000 miles. In order to form some faint concep- 



101. What subjects are treated of in Part II ? 

102. What figure does the sun present to us ? What angle 
would a line of 400 miles on the sun's disk subtend ? How is 
it inferred that the figure of the sun is spheroidal ? 



DENSITY. 71 

tion at least of this vast distance, let us reflect that a rail- 
way car, moving at the rate of 20 miles per horn', would 
require more than 500 years to reach the sun. 

The apparent diameter of the sun is a little more than 
half a degree, (32' 3^^.) Its linear diameter is about 
885,000 miles ; and since the diameter of the earth is 
only 7912 miles, the latter number is contained in the 
former nearly 112 times; so that it would require one 
hundred and twelve bodies like the earth, if laid side by 
side, to reach across the diameter of the sun ; and a ship 
sailing at the rate of ten miles an hour, would require 
more than ten years to sail across the solar disk. 

The sun is about 1,400,000 times as large as the earth. 
The distance of the moon from the earth being 238,000 
miles, were the center of the sun made to coincide with 
the center of the earth, the sun would extend every way 
from the earth nearly twice as far as the moon. 

104. In <ie?is%, the sun is only one-fourth that of the 
earth, being but a little heavier than water ; and the 
quantity of matter in the sun is three hundred and fifty 
thousand times as great as in the earth. A body would 
weigh nearly 28 times as much at the sun as at the 
earth. A man weighing 200 lbs. would, if transported 
to the surface of the sun, weigh 5,580 lbs., or nearly 2 J 
tons. To lift one's limb, would, in such a case, be be- 
yond the ordinary power of the muscles. At the surface 
of the earth, a body falls through I63L feet in a second ; 



103. "What is the distance of the sun from the earth ? How 
long would a railway car, moving at the rate of 20 miles per 
hour, require to reach the sun ? How many bodies equal to 
the earth could lie side by side across the sun ? How long 
would a ship be in sailing acros-s it at 10 miles an hour ? If 
the sun's center were made to coincide with the center of the 
earth, how much farther would it reach than the moon ? What 
is the sun's apparent diameter ? What is its linear diameter ? 

104. In density how does the sun compare with the earth? 
How in quantity of matter ? How much more would a body 
weigh at the sun than at the earth ? How far would a body 
fall in one second at the surface of the sun ? 



72 THE SUN. 

but a body would fall at the sun in one second through 
448.7 feet. 

SOLAR SPOTS. 

105. The surface of the sun, when viewed with a 
telescope, usually exhibits dark spots, which vary much, 
at different times, in number, figure, and extent. One 
hundred or more, assembled in several distinct groups, 
are sometimes visible at once on the solar disk. Tije 
greatest part of the solar spots are commonly very small, 
but occasionally a spot of enormous size is seen occupy- 
ing an extent of 50,000 miles in diameter. They are 
sometimes even visible to the naked eye, when the sun 
is viewed through colored glass, or, when near the hori- 
zon, it is seen through light clouds or vapours. When it 
is recollected that 1" of the solar disk implies an extent 
of 400 miles, it is evident that a space large enough to be 
seen by the naked eye, must cover a very large extent. 

A solar spot usually consists of two parts, the nucleus 
and the umbra, (Fig. 17.) The nucleus is black, of a 
Fig. 17. 




] 05. Solar spots. — Are they constant or variable in number 
and appearance 1 How many are sometimes seen on the sun's 
disk at once ? Are they usually large or small ? How many 
miles in diameter are the largest ? Describe a spot. What 
changes occur in the nucleus ? What is the umbra ? In what 
part of the sun do the spots mostly appear ? What apparent 
motions have thej ? What is the period of their revolution ? 



SOLAR SPOTS. 



73 



very irregular shape, and is subject to great and sudden 
changes, both in form and size. Spots have sometimes 
seemed to burst asunder, and to project fragments in dif- 
ferent directions. The umbra is a wide margin of 
lighter shade, and is often of greater extent than the 
nucleus. The spots are usually confined to a zone ex- 
tending across the central regions of the sun, not exceed- 
ing 60^ in breadth. When the spots are observed* from 
day to day, they are seen to move across the disk of the 
sun, occupying about two weeks in passing from one 
limb to the other. After an absence of about the same 
period, the spot returns, having taken 27d. 7h. 37m. in 
the entire revolution. 



106. The spots must be nearly 
or quite in contact with the body 
of the sun. Were they at any 
considerable distance from it, the 
time during which they would 
be seen on the solar disk, would 
be less than that occupied in 
the remainder of the revolution. 
Thus, let S, (Fig. 18,) be the 
sun, E the earth, and ahc the path 
of the body, revolving about 
the sun. Unless the spot were 
nearly or quite in contact with 
the body of the sun, being pro- 
jected upon his disk only vrhile 
passing from h to c, and being 
invisible while describing the 
arc cab, it would of course be 
out of sight longer than in sight, 
whereas the two periods are 
found to be equal Moreover, 



Fig. 18. 




106. How are the spots known to be nearly or quite in con- 
tact with the body of the sun ? Ilkistrate by figure 18. What 
causes the motion of the spots ? What is the period of the sun's 
revolution on his axis ? Explain by figure 19. 
7 



74 



the lines which all the solar spots describe on the disk 
of the sun, are found to be parallel to each other, like 
the circles of diurnal revolution around the earth, and 
hence it is inferred that they arise from a similar cause, 
namely, the revolution of the sun on its axis, a fact which 
is thus made known to us. 

But although the spots occupy about 27-J- days in pass- 
ing from one limb of the sun around to the same limb 
again, yet this is not the period of the sun's revolution 
on his axis, but exceeds it by nearly two days. For, 
let AA^B (Fig. 19,) represent the sun, and EE'M the 
orbit of the earth. Thus, when the earth is at E, the 
visible disk of the sun will be 
AA'B ; and if the earth remain- 
ed stationary at E, the time oc- 
cupied by a spot after leaving A 
until it returned to A, would be 
just equal to the time of the 
sun's revolution on his axis. 
But during the 27\ days in 
which the spot has been per- 
forming its apparent revolution, 
the earth has been advancing 
in his orbit from E to E', where 
the visible disk of the sun is 

A'B^ Consequently, before the spot can appear again 
on the limb from which it set out, it must describe so 
much more than an entire revolution as equals the arc 
AA^, and this occupies nearly two days, which sub- 
tracted from 27\ days, makes the sun's revolution on 
its axis about 25j days ; or more accurately, it is 25d. 
9h. 56m. 




107. A telescope of moderate powers is sufficient to 
show the spots on the sun, and it is earnestly recom- 
mended to the learner to avail himself of the first oppor- 



107. How large a telescope is sufficient to view the spots on 
the sun ? How is the eye protected from the glare of the sun's 
light ? How may these shades be made '' 



SOLAR SPOTS. rd 

tunity he may have, to view them for himself. For ob- 
servations on the sun, telescopes are usually furnished 
with colored glass shades, which are screwed upon the 
end of the instrument to which the eye is applied, for 
the purpose of protecting the eye from the glare of the 
sun's light. Such screens may be easily made by hold- 
ing a small piece of window glass over the flame of a 
lamp, the wick being raised higher than usual so as to 
smoke freely. 

108. The cause of the solar spots is unknown. It is 
not easy to determine what it is that occasions such 
changes on the surface of the sun ; but various conjec- 
tures have been proposed by different astronomers. Ga- 
lileo supposed that the dark part of a spot is owing to 
black cinders which rise from the interior of the sun, 
where they are formed by the action of heat, constitu- 
ting a kind of volcanic lava that floats upon the surface 
of the iiery flood, which he supposed to constitute the 
outer portion of the sun. But the vast extent which 
these spots occasionally assume is unfavourable to such a 
supposition. It is incredible that a quantity of volcanic 
lava should suddenly rise to the surface of the sun, suffi- 
cient to occupy (as a spot is sometimes found to do) 
2000,000,000 square miles. 

Dr. Herschel proposed a theory respecting the nature 
and constitution of the sun, which, more from respect 
to his authority than on account of any evidence by 
Yvhich it is supported, has been generally received. Ac- 
cording to him, the sun is itself an opake body like the 
earth, but is enveloped at a considerable distance from 
his body by tw^o different strata of clouds, the exterior 



108. Is the cause of solar spots well known ? What was 
Galileo's hypothesis ? What obje-ctions are there against it ? 
What is Herschel's theory of the nature and constitution of 
the sun ? What sort of a body does he consider the sun itself? 
By what is it encompassed ? Where is the repository of the 
sun's light and heat 1 How does he explain the spots ? What 
objections are there to this theory 1 What are facul<2 1 



76 THE SUN. 

stratum being the fountain from which emanates the 
sun's Hght and heat. The solar spots arise from the oc- 
casional displacement of portions of this envelope of 
clouds, disclosing to view tracts of the solid body of the 
sun. 

We regard this view of the origin of the sun's light and 
heat as unsubstantiated by any satisfactory proofs, and 
as in itself highly improbable. Such a medium would 
be a very unsuitable repository for the intense heat of 
the sun, which can arise only from fixed matter in a state 
of high ignition. The most probable supposition is, that 
the surface of the sun consists of melted matter in such 
a state. We must confess our ignorance of any known 
cause which is adequate to explain the sudden extinc- 
tion and removal of so large portions of this fiery fiood, 
as is occupied by some of the solar spots. 

Besides the dark spots on the sun, there are also seen, 
in difierent parts, places that are brighter than the neigh- 
boring portions of the disk. These are caWed facu/ce. 
Other inequalities are observable in powerful telescopes, 
all indicating that the surface of the sun is in a state of 
constant and powerful agitation. 

ZODIACAL LIGHT. 

109. The Zodiacal Light is a faint light resembling 
the tail of a comet, and is seen at certain seasons of the 
year following the course of the sun after evening twi- 
light, or preceding his approach in the morning sky. 
Figure 20 represents its appearance as seen in the even- 
ing in March, 1836. The following are the leading facts 
respecting it. 

1. Its form is that of a luminous pyramid, having its 
base towards the sun. It reaches to an immense dis- 
tance from the sun, sometimes even beyond the orbit of 
the earth. It is brighter in the parts nearer the sun than 
in those that are more remote, and terminates in an ob- 
tuse apex, its light fading away by insensible gradations, 
until it becomes too feeble for distinct vision. Hence 
its limits are at the same time fixed at different dis- 



ZODIACAL LIGHT. 



77 




tances from the sun by ditferent observers, according to 
their respective povvers of vision. 

2. Its aspects vary very much with the different seasons 
of the year. About the first of October, in our cUmate 
(Lat. 41° 18) it becomes visible before the dawn of day, 
rising along north of the ecliptic, and terminating above 
the nebula of Cancer. About the middle of November, 
its vertex is in the constellation Leo. At this time no 
traces of it are seen in the west after sunset, but about 
the first of December it becomes faintly visible in the 
west, crossing the Milky Way near the horizon, and 
reaching from the sun to the head of Capricornus, form- 
ing, as its brightness increases, a counterpart to the Milky 



af 



109. Zodiacal Light. —B escribe it. When and where 
seen ? What is its form ? How far does it reach ? Where 
brightest 1 How do its aspects vary at different seasons 
the°year 1 What motions has it ? Is it equally conspicuous 
every year ? What was it formerly held to be 1 With what 
phenomenon has it been supposed to be connected ^ 



78 THE SUN. 

Way, between which on the right, and the Zodiacal 
Light on the left, lies a triangular space embracing the 
Dolphin. Through the month of December, the Zo- 
diacal Light is seen on both sides of the sun, namely, 
before the morning and after the evening twilight, some- 
times extending 50^ westward, and 70° eastward of the 
sun at the same time. After it begins to appear in the 
western sky, it increases rapidly from night to night, 
both in length and brightness, and withdraws itself from 
the morning sky, where it is scarcely seen after the 
month of December, until the next October. 

3. The Zodiacal Light moves through the heavens in 
the order of the signs. It moves with unequal velocity, 
being sometimes stationary and sometimes retrogade, 
while at other times it advances much faster than the 
sun. In February and March, it is very conspicuous in 
the west, reaching to the Pleiades and beyond ; but in 
April it becomes more faint, and nearly or quite disap- 
pears during the month of May. It is scarcely seen in 
this latitude during the summer months. 

4. It is remarkably conspicuous at certain periods of 
a few years, and then for a long interval almost disap- 
pears. 

5. The ZodJacal Light icas formerly held to he the 
atmosphere of the sun. But La Place has shown that 
the solar atmosphere could never reach so far from the 
sun as this light is seen to extend. It has been supposed 
by others to be a nebulous body revolving around the 
sun. The author of this work has ventured to suggest 
the idea, that the extraordinary Meteoric Showers, which 
at different periods visit the earth, especially in the 
month of November, may be derived from this body. 
See American Journal of Science, Vol. 29, p, 378. 



79 



CHAPTER II. 



OF THE APPARENT ANNUAL MOTION OF THE SUN- 
FIGURE OF THE EARTH's ORBIT. 



-SEASONS 



110. The revolution of the earth around the sun once 
a year, produces an apparent motion of the sun around 
the earth in the same period. When bodies are at such 
a distance from each other as the earth and the sun, a 
spectator on either would project the other body upon 
the concave sphere of the heavens, always seeing it on 
the opposite side of a great circle, 180^ from himself. 
Thus when the eai'th arrives at Libra (Fig. 21,) we see 

Fig. 21. 




the sun in the opposite sign Aries. When the earth 
moves from Libra to Scorpio, as we are unconscious of 
our own motion, the sun it is that appears to move from 
Aries to Taurus, being always seen in the heavens, where 



80 THE SUN. 

a line drawn from the eye of the spectator through the 
body meets the concave sphere of the heavens. Hence 
the line of projection carries the sun forward on one 
side of the ecliptic, at the same rate as the earth moves 
on the opposite side ; and therefore, although we are un- 
conscious of our own motion, we can read it from day to 
day in the motions of the sun. If we could see the stars 
at the same time with the sun, we could actually observe 
from day to day the sun's progress through them, as we 
observe the progress of the moon at night ; only the 
sun's rate of motion would be nearly fourteen times 
slower than that of the moon. Although we do not see 
the stars w^hen the sun is present, yet after the sun is set, 
we can observe that it makes daily progress eastward, 
as is apparent from the constellations of the Zodiac oc- 
cupying, successively, the western sky after sunset, pro- 
ving that either all the stars have a common motion east- 
ward independent of their diurnal motion, or that the 
sun has a motion past them, from west to east. We 
shall see hereafter abundant evidence to prove, that this 
change in the relative position of the sun and stars, is 
owing to a change in the apparent place of the sun, 
and not to any change in the stars. 

111. Although the apparent revolution of the sun is 
in a direction opposite to the real motion of the earth, as 
regards absolute space, yet both are nevertheless from 
west to east, since these terms do not refer to any direc- 
tions in absolute space, but to the order in which certain 
constellations (the constellations of the Zodiac) succeed 
one another. The earth itself, on opposite sides of its 
orbit, does in fact move towards directly opposite points 



110. What produces the apparent motion of the sun around 
the earth once a year ? How would a spectator on either body 
see the other ? When the earth is at Libra, where does the 
sun appear to be ? Explain figure 21 . If the stars were visi- 
ble in the day time, how could we determine the sun's path ? 
What change do the constellations of the Zodiac undergo with 
respect to the sun ? 



ANNUAL MOTION, 81 

of space ; but it is all the while pursuing its course in 
the order of the signs. In the same manner, although 
the earth turns on its axis from west to east, yet any 
place on the surface of the earth is moving in a direc- 
tion in space exactly opposite to its direction twelve 
hours before, if the sun left a visible trace on the face 
of the sky, the ecliptic would of course be distinctly 
marked on tJie celestial sphere as it is on an artificial 
globe ; and were the equator delineated in a similar man- 
ner, (by any method like that supposed in Art. 33,) we 
should then see at a glance the relative position of these 
two circles, the points where they intersect one another 
constituting the equinoxes, the points where they are at 
the greatest distance asunder, or the solstices, and vari- 
ous other particulars, which for want of such visible 
traces, w^e are now obliged to search for by indirect and 
circuitous methods. It will even aid the learner to have 
constantly before his mental vision, an imaginary delin- 
eation of these two important circles on the face of the 
sky. 

112. The equator makes an angle with the ecliptic oj 
23° 28'. This is called the obhquity of the ecliptic. 
As the sun and earth are both always in the ecliptic, and 
as the motion of the earth in one part of it makes the 
sun appear to move in the opposite part at the same rate, 
the sun apparently descends in the winter 23° 28' to the 
south of the equator, and ascends in the summer the 
same number of degrees to the north of it. We must 
keep in mind that the celestial equator and the celestial 
ecliptic are here understood, and we may imagine them 



111. In what sense are the motions of the sun and earth 
opposite, and in what sense in the same direction ? If the 
ecliptic and equator were distinctly delineated on the face of 
the sky, what points in them could be easily observed ? 

112. What angle does the equa,tor make with the ecliptic? 
In what circle do the sun and earth always appear ? How far 
do they recede from the equator ? How does the obliquity of 
the ecliptic vary ? 



82 THE SUN. 

to be two great circles distinctly delineated on the face 
of the sky. On comparing observations made at differ- 
ent periods for more than two thousand years, it is found, 
that the obliquity of the ecliptic is not constant, but 
that it undergoes a slight diminution from age to age, 
amounting to 52" in a century, or about half a second 
annually. We might apprehend that by successive ap- 
proaches to each other the equator and ecliptic would 
finally coincide ; but astronomers have found by a most 
profound investigation, founded on the principles of 
universal gravitation, that this variation is confined with- 
in certain narrow limits, and that the obliquity, after di- 
minishing for some thousands of years, will then in- 
crease for a similar period, and will thus vibrate for ever 
about a mean value. 

113. Let us conceive of the sun as at that point of the 
ecliptic where it crosses the equator, that is, at one of the 
equinoxes, as the vernal equinox. Suppose he stands 
still then for twenty four hours. The revolution of the 
earth on its axis from east to west during this twenty 
four hours, will make the sun appear to describe a great 
circle from east to west, coinciding with the equator. 
At the end of this period, suppose the sun to move 
northward one degree and to remain there for the next 
twenty-four hours, in which time the revolution of the 
earth will make the sun appear to describe another cir- 
cle from east to west, parallel to the equator, but one 
degree north of it. Thus we may conceive of the sun 
as moving one degree every day for about three months, 
when it will reach the point of the ecliptic farthest 
from the equator, which is called the tropic from a Greek 



113. Suppose the sun to start from the equator and to ad- 
vance one degree north daily, explain its apparent diurnal rev- 
olutions. When is the sun at the northern tropic ? When is 
he at the southern tropic ? How arc the respective meridian 
altitudes of the suu at these periods ? How do we find from 
these observations, the obliquity of the ecliptic ? 



THE SEASONS. S3 

word (rgsTiw) which signifies to turn, because when the 
sun arrives at this point, his motion in his orbit carries 
him continually towards the equator, and therefore he 
seems to turn about. 

When the sun is at the northern tropic, which hap- 
pens about the 21st of June, his elevation above the 
southern horizon at noon, is the greatest of the year ; 
and when he is at the southern tropic, about the 21st 
of December, his elevation at noon is the least in the 
year. The difference between these two meridian alti- 
tudes, will give the whole distance from one tropic to 
the other, and consequently twice the distance from each 
tropic to the equator. By this means we find how far 
the tropic is from the equator, and that gives us the in- 
clination of the two circles to one another ; for the great- 
est distance between any two great circles on the sphere, 
is always equal to the angle which they make with each 
other. 

114. The dimensions of the eartKs orbit, when com- 
'pared with its own magnitude, are immense. 

Since the distance of the earth from the sun is 
95,000,000 miles, and the length of the entire orbit nearly 
600,000,000 miles, it will be found, on calculation, that 
the earth moves 1,640,000 miles per day, 68,000 miles 
per hour, 1,100 miles per minute, and nearly 19 miles 
every second, a velocity nearly sixty times as great as 
the maximum velocity of a cannon ball. A place on 
the earth's equator turns, in the diurnal revolution, at the 
rate of about 1,000 miles an hour and j^ of a mile per 
second. The motion around the sun, therefore, is nearly 
seventy times as swift as the greatest motion around the 
axis. 



114. What is said of the dimensions of the earth's orbit ? 
At what rate does the earth move in its orbit per day, hour, 
minute, and second 1 How far does a place on the earth's 
equator move per hour and second 1 How much swifter is 
the motion in the orbit than on its axis ? 



84 THE SUN. 

THE SEASONS. 

115. TJie change of seasons depends on two causes, 
(1) the obliquity of the ecliptic, and (2) the earth's axis 
always remaining parallel to itself. Had the earth's 
axis been perpendicular to the plane of its orbit, the 
equator would have coincided with the ecliptic, and the 
sun would have constantly appeared in the equator. 
To the inhabitants of the equatorial regions, the sun 
would always have appeared to move in the prime ver- 
tical ; and to the inhabitants of either pole, he would 
always have been in the horizon. But the axis being 
turned out of a perpendicular direction 23^ 28', the 
equator is turned the same distance out of the ecliptic r 
and since the equator and ecliptic are two great circles 
which cut each other in two opposite points, the sun, 
while performing his circuit in the ecliptic, must evi- 
dently be once a year in each of those points, and must 
depart from the equator of the heavens to a distance on 
either side equal to the inclination of the two circles, 
that is, 23° 28'. 

116. The earth being a globe,, the sun constantly en- 
lightens the half next to him,* while the other half is in 
darkness. The boundai-y between the enlightened and 
unenlightened part, is called the circle of illumination. 
When the earth is at one of the equinoxes, the sun is at 
the other, and the circle of illumination passes through 
both the Doles. When the earth reaches one of the 



115. The Seasons. — On what two causes doos the change 
of seasons depend ? Had the earth's axis been perpendicu- 
lar to the plane of its orbit, in what great circle would the sun 
always have appeared to move ? 



* In fact, the sun enlightens a little more than half the earth, since 
on account of his vast magnitude the tangents drawn from opposite 
sides of the sun to opposite sides of the earth, converge to a point 
behind the earth, as will be seen by and by in the representation of 
eclipses. 



THE SEASONS. 



85 



tropics, the sun being at the other, the circle of illumin- 
ation cuts the earth, so as to pass 23° 28' beyond the 
nearer, and the same distance short of the remoter pole. 
These results would not be uniform, were not the earth's 
axis always to remain parallel to itself. The following 
figure will illustrate the foregoing statements. 
Fig. 22. 




Let ABCD represent the earth's place in different 
parts of its orbit, having the sun in the center. Let A, 



116. How much of the earth does the sun enlighten at once ? 
Define the circle of illumination. How does it cut the earth at 
the equinoxes ? How at the solstices ? Explain figure 22. 
When the earth is at one of the tropics and the sun at the 
other, where is it continual day and where continual night ? 
8 



86 THE SUN. 

C, be the positions of the earth at the equinoxes, and B, 

D, its positions at the tropics, the axis ns being always 
parallel to itself.* At A and C the sun shines on both 
n and s ; and now let the globe be turned round on its 
axis, and the learner will easily conceive that the sun 
will appear to describe the equator, which being bisected 
by the horizon of every place, of course the day and 
night will be equal in all parts of the globe. f Again, 
at B when the earth is at the southern tropic, the sun 
shines 23i° beyond the north pole n, and falls the same 
distance short of the south pole s. The case is exactly 
reversed when the earth is at the northern tropic and 
the sun at the southern. While the earth is at one of 
the tropics, at B for example, let us conceive of it as turn- 
ing on its axis, and we shall readily see that all that part 
of the earth which lies within the north polar circle will 
e-njoy continual day, while that within the south polar 
circle w^ill have continual night, and that all other places 
will have their days longer as they are nearer to the en- 
lightened pole, and shorter as they are nearer to the un- 
enlightened pole. This figure likewise show^s the suc- 
cessive positions of the earth at different periods of the 
year, with respect to the signs, and w^hat months corres- 
pond to particular signs. Thus the earth enters Libra 
and the sun Aries on the 21st of March, and on the 21st 
of June the earth is just entering Capricorn and the sun 
Cancer. 

117. Had the axis of the earth been perpendicular 
to the plane of the ecliptic, then the sun would always 
have appeared to move in the equator, the days would 
every where have been equal to the nights, and there 
could have been no change of seasons. On the other 
hand, had the inclination of the ecliptic to the equator 



* The learner will remark that the hemisphere towards n is above, 
and that towards s is below the plane of the paper. It is important to 
form a just conception of the position of the axis with respect to the 
plane of its orbit. 

t At the pole, the solar disk, at the time of the equinox, appears bis- 
ected by the horizon. 



THE SEASONS. 87 

been much greater than it is, the vicissitudes of the sea- 
sons would have been proportionally greater than at pres- 
ent. Suppose, for instance, the equator had been at 
right angles to the ecliptic, in which case the poles of 
the earth would have been situated in the ecliptic itself; 
then in different parts of the earth the appearances 
would have been as follows. To a spectator on the 
equat6r, the sun as he left the vernal equinox would 
every day perform his diurnal revolution in a smaller 
and smaller circle, until he reached the north pole, when 
he would halt for a moment, and then wheel about and 
retui'n to the equator in the reverse order. The pro- 
gress of the sun through the southern signs, to the south 
pole, would be similar to that already described. Such 
would be the appearances to an inhabitant of the equa- 
torial regions. To a spectator living in an oblique 
sphere, in our own latitude for example, the sun while 
north of the equator would advance continually north- 
ward, making his diurnal circuits in parallels farther and 
farther distant from the equator, until he reached the 
circle of perpetual apparition, after which he would 
cKmb by a spiral course to the north star, and then as 
rapidly return to the equator. By a similar progress 
southward, the sun would at length pass the circle of 
perpetual occultation, and for some time (which would 
be longer or shorter according to the latitude of the place 
of observation) there would be continual night. 

f he great vicissitudes of heat and cold which would 
attend such a motion of the sun, would be wholly in- 
compatible with the existence of either the animal or 
the vegetable kingdoms, and all terrestrial nature would 



117. Had the earth's axis been perpendicular to the plane ^ 
of the ecliptic, would there have been any change of seasons ? 
What would have been the consequence had the equator been 
at right angles to the ecliptic ? How would the sun appear to 
move to a person on the equator ? How to one situated at the 
pole 1 How to an inhabitant of an oblique sphere 'I How 
would have been the vicissitudes of heat and cold ? 



88 THE SUN. 

be doomed to perpetual sterility and desolation. The 
happy provision which the Creator has made against 
such extreme vicissitudes, by confining the changes of 
the seasons within such narrow bounds, conspires with 
many other express arrangements in the economy of 
nature to secure the safety and comfort of the human 
race. 

FIGURE OF THE EARTH's ORBIT. 

118. Thus far we have taken the earth's orbit as a 
great circle, such being the projection of it on the celes- 
tial sphere ; but we now proceed to investigate its actual 
figure. 

Fig. 23. 




Were the earth's path a circle, having ihe sun in the 
center, the sun would always appear to be at the same 



118. Were the earth's path a circle, how would the distance 
of the sun from us always appear ? Define the radius vector. 
What do we infer from the fact that the radius vector is con- 
stantly varying ? How do we learn the relative distances of 
the earth ? How do wo construct a figure representing the 
earth's orbit ? Explain figure 23. 



FIGURE OF THE EARTh's ORBIT. 89 

distance from us ; that is, the radius of its orbit, or ra- 
dius vector, the name given to a hne drawn from the 
center of the sun to the orbit of any planet, would al- 
ways be of the same length. But the earth's distance 
from the sun is constantly varying, which shows that 
its orbit is not a circle. We learn the true figure of the 
orbit, by ascertaining the relative distances of the earth 
from the sun at various periods of the year. These all 
being laid down in a diagram, according to their respec- 
tive lengths, the extremities, on being connected, give 
us our first idea of the shape of the orbit, which appears 
of an oval form, and at least resembles an ellipse ; andy 
on further trial, we find that it has the properties of an 
elHpse. Thus, let E (Fig. 23,) be the place of the 
earth, and a, b, c, 6dc. successive positions of the sun ; 
the relative lengths of the lines E<^, Et>, &:c. being 
known : on connecting the points, a, b, c, &c. the result- 
ing figure indicates the true shape of the earth's orbit. 

119. These relative distances are found in tv/o differ- 
ent ways ; first, by changes in the surCs apparent diam- 
eter, and, secondly, by variations in his angular velo- 
city. The same object appears to us smaller in propor- 
tion as it is more distant ; and if we see a heavenly body 
varying in size at different times, we 'infer that it is at 
different distances from us ; that when largest, it is near- 
est to us, and when smallest, farthest off. Now v/hen 
the sun's diameter is measured accurately by instru- 
ments, it is found to vary from day to day, being when 
greatest more than thirty-two minutes and a half, and 
when smallest only thirty-one minutes and a half, differ- 
ing in all, about seventy-five seconds. When the diam- 
eter is greatest, which happens in January, we know 



119. How does the same body appear when at different dis- 
tances ? What inferences do we make from its variations of 
size ? How much does the apparent diameter of the sun vary 
in difierent parts of the year ? When is it greatest, and 
when smallest 1 Define the terms perihelion and aphelion. 



90 THE SUN. 

that the sun is nearest to us ; and when the diameter is 
least, which occurs in July, we infer that the sun is at 
the greatest distance from us. 

The point where the earth or any planet, in its revo- 
lution, is nearest the sun, is called its perihelion ; the 
point where it is farthest from the sun, its aphelion, 

120. Similar conclusions may be drawn from obser- 
vations on the sun's angular velocity. A body appears 
to move most rapidly when nearest to us. Indeed the 
apparent velocity of the sun increases rapidly as it ap- 
proaches us, and as rapidly diminishes when it recedes 
from us. If it were to come twice as near as before it 
w-ould appear, to move not merely twice as swift, but 
four times as swift ; if it came ten times nearer, its appa- 
rent velocity would be one hundred times as great as 
before. We say, therefore, that the velocity varies 
inversely as the square of the distance, for as the dis- 
tance is diminished ten times, the velocity is increased 
the square of ten, that is, one hundred times. Now by 
noting the time it takes the sun, from day to day, to re- 
turn to the meridian, v/e learn the comparative veloci- 
ties wdth which it moves at different times, and from 
these we derive the comparative distances of the sun 
at the corresponding times. 

When by either of the foregoing methods, we have 
learned the relative distances of the sun from the earth 
at various periods of the year, we may lay down, or plot 
in a diagram hke figure 23, a representation of the orbit 
which the sun apparently describes about the earth, and 
it will give us the figure of the orbit which the earth 
really describes about the sun, in its annual revolution. 



120. What conclusions are drawn from the variations in 
the sun's angular velocity ? According to what law does the 
velocity vary ? How may we ascertain the sun's daily rate ? 
What great doctrine is it necessary to be acquainted with, in 
order to understand the celestial motions ? 



UNIVERSAL GRAVITATION. 91 

But neither the revolution of the earth about the sun, 
nor indeed that of any of the planets, can be well and 
clearly understood, until we are acquainted with the 
forces by which their motions are produced, especially 
w^ith the doctrine of Universal Gravitation. To this 
subject, therefore, let us next apply our attention. 



CHAPTER III. 

OF UNIVERSAL GRAVITATION KEPLEr's LAWS MOTION 

IN AN ELLIPTICAL ORBIT PRECESSION OF THE EQUI- 
NOXES. 

121. We discover in nature a tendency of every por- 
tion of matter towards every other. This tendency is 
called gravitation. In obedirence to this power, a stone 
falls to the ground and a planet revolves aground the sun. 

It was once supposed that we could not reason from 
the phenomena of the earth to those of the heavens ; 
since it vv^as held that the laws of motion might be 
very different among the heavenly bodies from what 
we find them to be on this globe ; but Galileo and New- 
ton in their researches into nature, proceeded on the 
idea that nature is uniform in all her works, and that 
every where the same causes produces the same effects, 
and that the same effects result from the same causes. 
That this is a sound principle of philosophy, is proved 
by the fact, that all the conclusions derived from it in 
the interpretation of nature are found to be true. Hence 
by studying the laws of motion as exhibited constantly 
before our eyes in all terrestrial motions, v/e are learning 



121. What force do we observe in nature ? What is this 
force called ? Can we reason from terrestrial to celestial phe- 
nomena ? On what idea did Galileo and Newton proceed ? 
How is this proved to be a sound principle of philosophy 1 



92 UNIVERSAL GRAVITATION. 

the laws that govern the movements of the heavenly 
bodies. 

122. On the earth all bodies are seen to fall towards 
its center. A stone let fall in any part of the earth, de- 
scends immediately to the ground. This may seem to 
the young learner as so- much a matter of course as to 
require no explanation. But stones fall in exactly op- 
posite directions on opposite sides of the earth, always 
falling towards the center of the earth from every part 
exterior to its surface; as when '^ 
we hold a small needle towards 
a magnetic ball or load stone, the 
needle v»^ill fly towards the ball, 
and cling to its surface, to w^hich- 
ever side of the ball it is present- 
ed. (Fig. 24.) From this uni- 
versal descent of bodies near the 
earth, w^e infer the existence of 
some force which draws or impels them, and this invisi- 
ble force we call the attraction of gravitation, or simply 
gravity. 

123. By the laws of gravity v,^e mean the manner in 
w^hich it always acts. They are three in number, and 
are comprehended in the following proposition : 

Gravity acts on all matter alike, with a force projjor- 
tioned to the quantity of matter, and inversely as the 
square of the distance. 

First, gravity acts on all matter alike. Every body 
in nature, whether great or small, whether solid,' liquid, 
or aeriform, exhibits the same tendency to fall towards 
the center of the earth. Some bodies, indeed, seem less 
prone to fall than others, and some even appear to rise, 
as smoke and light vapors. But this is because they are 
supported by the air ; when that is removed, they de- 




122, In what directions do bodies fall in all parts of the 
earth ? Illustrate by figure 24. What is gravity ? 



LAWS OF GRAVITY. 93 

scend alike towards the earth ; a guinea and a feather, 

the lightest vapor and the heaviest rocks, fall with equal 
velocities. 

Secondly, the force of gravity is proportioned to the 
quantity of matter. A mass of lead contains perhaps 
fifty times as much matter as an equal bulk of cotton'; 
yet, if carried beyond the atmosphere, and let fall in ab- 
solute space, they would both descend towards the earth 
with equal speed, until they entered the atmosphere, 
and were the atmosphere removed they would continue 
to fall side by side until they reached the earth. Now 
if the lead contains fifty times as much matter as the 
cotton, it must take fifty times the force to make it move 
w^ith equal velocity. If we double the load we must 
double the team, if we would continue to travel at the 
same speed as before. Hence, from the fact that bodies 
of various degrees of density descend alike towards the 
center of the earth by the force of gravity, we infer 
that that force is always exerted upon bodies in exact 
proportion to their quantity of matter. 

Thirdly, the force with which gravity acts upon bod- 
ies at difierent distances from the earth, is inversely as 
the square of the distance from the center of the earth. 
If a pound of lead were carried as far above the earth as 
from the center to the surface of the earth, it would 
weigh only one-fourth of a pound ; for being twice as 
far as before from the center of the earth, its weight 
would be diminished in the proportion of the square of 
two, that is, four times. 



123. What do we mean by the law of gra"VT.ty 1 State the 
general proposition. Show that gravity acts on all matter alike. 
How is this consistent with the fact, that some bodies appear to 
rise ? How would all bodies fall in a vaciumi ? Explain how 
gravity is proportioned to the quantity of m.atter. How would 
equal masses of lead and cotton fall, if carried beyond the at- 
mosphere ? What do we infer from the fact, that all bodies fall 
towards the earth with equal velocities ? To what is gravity 
acting at different distances proportioned ? How much would 
a pound of lead weigh, if carried as far above the earth as from 
the surface to the center ? 



94 UNIVERSAL GRAVITATION. 

124. Bodies falling to the earth by gravity have their 
velocity continually increased. For since they retain 
what motion they have and constantly receive more 
by the continued action of gravity, they must move 
faster and faster, as a wheel has its velocity constantly 
accelerated when we continue to apply successive im- 
pulses to it. 

The spaces which bodies describe, when falling freely 
by gravity, are as the squares of the times. It is found 
by experiment, that a body will fall from a state of 
rest 16 j2 f^^t in one second. In two seconds it will not 
fall merely through double this space, but through four 
times this space, that is, through a distance expressed 
by the square of the time multiplied into 16-/3. Conse- 
quently, in two seconds the fall will be 641-, in three se- 
conds 144J, and in ten seconds 1608i feet, that is, 
through one hundred times 163^2 ^^^t- 

The weight of a body is nothing more than the ac- 
tion of gravity upon it tending to carry it towards the 
center of the earth. The counterpoise which is placed 
in the opposite scale by which its weight is estimated, is 
the force it takes to hold the body hack, which must be 
just equal to that by which it endeavors to descend. 

125. There is another principle which it is necessary 
clearly to comprehend before we can understand the mo- 
tions of the heavenly bodies. It is commonly called the 
First Law of Motion and is as follows : 

Every body perseveres in a state of rest, or of unform 
motion in a straight line, unless compelled by some force 
to change its state. This law has been fully established 
by experiment, and is conformable to all experience. 
It embraces several particulars. First, A body when at 



124. When a body is falling towards the earth, how is its 
velocity affected ? To what are the spaces described by fall- 
ing bodies proportioned ? How far will a body fall from a state 
of rest in one second 1 How far in two seconds ? What is 
the weight of a body ? 



LAWS OF MOTION. 95 

rest remains so unless some force puts it in motion ; 
and hence it is inferred, when a body is found in mo- 
tion, that some force must have been apphed to it suffi- 
cient to have caused its motion. Thus, the fact that 
the earth is in motion around the sun and around its ov^^n 
axis, is to be accounted for by assigning to each of these 
motions a force adequate, both in quantity and direction, 
to produce these motions respectively. 

Secondly, When a body is once in motion it will con- 
tinue to move forever, unless something stops it. When 
a bail is struck on the surface of the earth, the friction 
of the earth and the resistance of the air soon stop its 
motion ; when struck on smooth ice it will go much 
farther before it comes to a state of rest, because the ice 
opposes much less resistance than the ground ; and were 
there no impediment to its motion it would, when once 
set in motion, continue to move without end. The 
heavenly bodies are actually in this condition : they 
continue to move, not because any new forces are ap- 
plied to them, but, having been once set in motion, they 
continue in motion because there is nothing to stop them. 

Thirdly, The motion to which a body naturally tends 
is uniform ; that is, the body moves just as far the se- 
cond minute as it did the first, and as far the third as 
the second, passing over equal spaces in equal times. 

Fourthly, A body in motion will move in a straight 
line, unless diverted out of that line by some external 
force ; and the body will resume its straight forward mo- 
tion, when ever the force that turns it aside is with- 
drawn. Every body that is revolving in an orbit, like 
the moon around the earth, or the earth around the sun, 



125. Recite the first law of motion. How has this law been 
established ? What does the fact, that the earth is in motion 
around the sun imply? How would a ball when once struck 
continue to move, if it met with no resistance ? Why do the 
heavenly bodies continue to move ? What is meant by saying 
that motion is naturally uniform 1 In what direction does 
every revolving bodv tend to move. 



96 UNIVERSAL GRAVITATION. 

tends to move in a straight line which is a tangent* to 
its orbit. 

' Let us now see how the foregoing principles, which 
operate upon bodies on the earth, are extended so as to 
embrace all bodies in the universe, as in the doctrine of 
Universal Gravitation. This important principle is thus 
defined : 

126. Universal gravitation, is that influence by 
which every body in the universe, ivhcther great or small, 
tends towards every others with a force which is directly 
as the quantity of matter, and inversely as the square of 
the distance. 

As this force acts as though bodies were drawn to- 
wards each other by a mutual attraction, the force is de- 
nominated attraction; but it must be borne in mind, 
that this term is figurative, and implies nothing respect- 
ing the nature of the force. 

The existence of such a force in nature was distinctly 
asserted by several astronomers previous to the time of 
Sir Isaac Newton, but its laws were first promulgated 
by this wonderful man in his Principia, in the year 1687. 
It is related, that while sitting in a garden, and musing 
on the cause of the falling of an apple, he reasoned 
thus '.■\ that, since bodies far removed from the earth fall 
towards it, as from the tops of towers, and the highest 
mountains, why ma}^ not the same influence extend 
even to the moon ; and if so, may not this be the reason 
why the moon is made to revolve around the earth, as 
would be the case with a cannon ball were it projected 
horizontally near the earth with a certain velocity. Ac- 
cording to the first law of motion, the moon, if not con- 
tinually drawn or impelled towards the earth by some 
force, would not revolve around it, but would proceed 
on in a straight line. But going around the earth as she 
does, in an orbit that is nearly circular, she must be 



* A tangent is a straight line which touches a curve. Thus AB (Fig 
25,) is a tangent to the circle at A. 

t Pemberton's View of Newton's Philosophy. 



UNIVERSAL BRAVITATION. 



97 



urged towards the earth by some force, which diverts 
her from a straight course. For let the earth (Fig. 25,) 
be at E, and let the arc described by the moon in one 
second of time be Ab. Were the moon influenced by 
no extraneous force, to turn aside, she would have de- 
scribed, not the arc Ah, but the straight line AB, and 
would have been found at the end of the given time at 
B instead of h. She therefore departs from the line in 
which she tends naturally to move, by the line B&, 
which in small angles may be taken as equal to Ka> 
Fig. 25. 




This deviation from the tangent must be owing to some 
extraneous force. Does this force correspond to what 
the force of gravity exerted by the earth, would be at 
the distance of the moon ? The question resolves itself 
into this : Would the force of gravity exerted by the 
earth upon the moon, cause the moon to deviate from 
her straight forward course towards the earth just as 
much as she is actually found to deviate ? Now we 



126. Universal Gravitation. — Define it. Why called at- 
traction ? State the historical facts connected with its discov- 
ery. How did Sir Isaac Newton reason from the falling of an 
apple 1 Explain by figure 25. How is it proved that gravity 
and no other force causes the moon to revolve about the earth ? 
9 



98 UNIVERSAL GRAVITATION. 

know how far the moon is from the earth, namely, sixty 
times as far as it is from the center to the surface of the 
earth ; and since the force of gravity decreases in pro- 
portion to the square of the distance, this force must be 
3600 times (which equals the square of GO,) less than at 
the surface of the earth. This is found, on computa- 
tion, to be exactly the force required to make the moon 
deviate to the amount she does from the straight line in 
which she constantly tends to move ; and hence it is 
inferred that gravity, and no other force than gravity, 
causes the moon to circulate around the earth. 

By this process it was discovered that the law of grav- 
itation extends to the moon. By subsequent inquiries 
it was found to extend in like manner to all the planets, 
and to every member of the solar system ; and, finally, 
recent investigations have shown that it extends to the 
fixed stars. The law of gravitation, therefore, is now 
established as the grand principle which governs all the 
motions of the heavenly bodies. 



KEPLER'S LAWS. 

127. There are three great principles, according to 
which the motions of the earth and all the planets 
around the sun are regulated, called Kepler's Laws, hav- 
ing been first discovered by the great astronomer whose 
name they bear. They may appear to the young learner, 
when he first reads them, dry and obscure ; yet they 
will be easily understood from the explanations that fol- 
low ; and so important have they proved in astronomical 
inquiries, that they have acquired for their renowned 
discoverer the exalted appellation of the legislator of the 
skies. 

We will consider each of these laws separately. 



127. Kepler's Laws. — Why so called ? What appellation 
has been given to Kepler ? 



KEPLER S LAWS. 



99 



128. First law. The orbits of the earth and all the 
planets are ellipses ^ having the sun in the common 
focus. 

In a circle all the diameters are equal to each other ; 
but if we take a metallic wire or hoop and draw it out on 
opposite sides, we elongate it into an ellipse, of which the 
different diameters are very unequal. That which con- 
nects the two points most distant from each other is called 
the transverse, and that which is at right angles to this 
is called the conjugate axis. Thus AB (Fig. 26) is the 




transverse axis and CD the conjugate of the ellipse AB. 
By such a process of elongating the circle into an el- 
lipse, the center of the circle may be conceived of as 
drawn opposite ways to E and F, each of which be- 
comes 2i focus, and both together are called the foci of the 
ellipse. The distance GE or GF of the focus from the 



128. Becite the first law. In a circle, how are all the diam- 
eters 1 How are they in an ellipse 1 What is the longest di- 
ameter called ■? What is the shortest called 1 Explain by figure 
26. What is the eccentricity of the elHpse 1 How many el- 
lipses may there be having a common focus 1 Explain figure 
26, How eccentric is the earth's orbit ? 



100 UNIVERSAL GRAVITATION. 

center is called the eccentricity of the ellipse ; and the 
ellipse is said to be more or less eccentric, as the distance 
of "the focus from the center is greater or less. 

Now there may be an indefinite number of ellipses 
having one common focus, but varying greatly in ec- 
centricity. Figure 27 represents such a collection of 




ellipses around the common focus F, the innermost AGD 
having a small eccentricity or varying little from a cir- 
cle, while the outermost ACB is a very eccentric ellipse. 
The orbits of all the bodies that revolve about the sun, 
both planets and comets, have, in like manner, a com- 
mon focus in which the sun is situated, but they differ 
in eccentricity. 

Most of the planets have orbits of very little eccen- 
tricity, differing little from circles, but comets move in 
very eccentric ellipses. 

The earth's path around the sun varies so little from 
a circle, that a diagram representing it truly would 
scarcely be distinguished from a perfect circle ; yet 
when the comparative distances of the sun from the 
earth are taken at different seasons of the year, as is ex- 
plained in Art. 118, we find that the difference between 



^ 



Kepler's laws. 101 

the greatest and least distances is no less than 3,000,000 
miles. 

129. Second law. The radius vector of the earth, 
or of any planet, describes equal areas in equal times. 

It will be recollected that the radius vector is a line 
drawn from the center of the sun to a planet revolving 
about the sun, (Art. 118.) Thus Ea, Eb, Ec, (Fig. 23,) 
&c. are successive representations of the radius vector. 
Now if a planet sets out from a and travels round the sun 
in the direction ofabc, it will move faster when nearer the 
sun, as at a, than when more remote from it, as at m ; 
yet if ah and mn be arcs described in equal times, then, 
according to the foregoing law, the space Eab will be 
equal to the space Emn ; and the same is true of all the 
other spaces described in equal times. Although the 
figure Eab is much shorter than Emn, yet its greater 
breadth exactly counterbalances the greater length of 
those figures which are described by the radius vector 
where it is longer. 

130. Third law. The squares of the periodical times 
are as the cubes of the mean distances from the sun. 

The periodical time of a body is the time it takes to 
complete its orbit in its revolution about the sun. Thus 
the earth's periodic time is one year, and that of the 
planet Jupiter is about twelve years. As Jupiter takes 
so much longer time to travel round the sun than the 
earth does, we might suspect that his orbit was larger 
than that of the earth, and of course that he was at 
a greater distance from the sun, and our first thought 
might be that he was probably twelve times as far off; 
but Kepler discovered that the distances did not increase 
as fast as the times increased, but that the planets which 



129. State Kepler's second law. Explain byfigure 23, p. 88. 

130. State Kepler's third law. What is meant by the peri- 
odical time of a body ? Do planets move faster or slower as 
they are more distant from the sun 1 Explain the law. 

9* 



102 UNIVERSAL GRAVITATION. 

are more distant from the sun actually move slower than 
those which are nearer. After trying a great many pro- 
portions, he at length found that if we take the squares 
of the periodic times of two planets, the greater square 
contains the less, just as often as the cube of the dis 
tance of the greater contains that of the less. This fact 
is expressed by saying, that the squares of the periodic 
times are to one another as the cubes of the distances. 
This law is of great use in determining the distances 
of all the planets from the sun, as we shall see more fully 
hereafter. 

MOTION IN AN ELLIPTICAL ORBIT. 

131. Let us now endeavor to gain a just conception 
of the forces by which the earth and all the planets are 
made to revolve about the sun. 

In obedience to the first law of motion, every moving 
body tends to move in a straight line ; and were not the 
planets deflected continually towards the sun by the 
force of attraction, these bodies as well as others would 
move forward in a rectilineal direction. We call the force 
by which they tend to such a direction the projectile 
force, because its effects are the same as though the body 
were originally projected from a certain point in a certain 
direction. It is an interesting problem for mechanics to 
solve, what was the nature of the impulse originally 
given to the earth, in order to impress upon it its two 
motions, the one around its own axis, the other around 
the sun. If struck in the direction of its center of 
gravity it might receive a forward motion, but no rota- 
tion on its axis. It must, therefore, have been impelled 
by a force, whose direction did not pass through its 



131. Explain how a body is made to rerolve in an orbit, 
under the action of two forces. What is meant by the projec- 
tile force ? How must the earth have been impelled in order 
to receive its present motions ? How illustrated by the mo- 
tions of a top ? 



MOTION IN AN ELLIPTICAL ORBIT. 103 

center of gravity. Bernouilli, a celebrated mathemati- 
cian, has calculated that the impulse must have been 
given very nearly in the direction of the center, the 
point of projection being only the 165th part of the 
earth's radius from the center. This impulse alone 
would cause the earth to move in a right line : gravita- 
tion towards the sun causes it tt) describe an orbit. 
Thus a top spinning on a smooth plane, as that of glass 
or ice, impelled in a direction not coinciding with that 
of the center of gravity, may be made to imitate the two 
motions of the earth, especially if the experiment is tried 
in a concave surface like that of a large bowl. The re- 
sistance occasioned by the surface on which the top 
moves, and that of the air, will gradually destroy the 
force of projection and cause the top to revolve in a 
smaller and smaller orbit ; but the earth meets with no 
such resistance, and therefore makes both her days and 
years of the same length from age to age. A body, 
therefore, revolving in an orbit about a center of attrac- 
tion, is constantly under the influence of two forces, — 
the projectile force, which tends to carry it forward in a 
straight line which is a tangent to its orbit, and the cen- 
tripetal force, by which it tends towards the center. 

132. As an example of a body revolving in an orbit 
under the influence of two forces, suppose a body pla- 
ced at any point P (Fig. 28,) above the surface of the 
earth, and let PA be the direction of the earth's center. 
If the body were allowed to move without receiving 
any impulse, it would descend to the earth in the direc- 
tion PA with an accelerated motion. But suppose that 
at the moment of its departure from P, it receives an 
impulse in the direction PB, which would carry it to B 
in the time the body would fall from P to A ; then un- 
der the influence of both forces it would descend along 
the curve PD. If a stronger impulse w^ere given it in 



132. Explain figure 28. How might a body be made to 
circulate quite around the earth ? 



104 



UNIVERSAL GRAVITATION. 




the direction PB, it would describe a larger curve PE, 
or PF, or finally, it would go quite round the earth and 
return again to P. 

133. The most simple example we have of the com- 
bined action of these two forces, is the motion of a mis- 
sile thrown from the hand, or of a ball fired from a can- 
non. It is well known that the particular form of the 
curve described by the projectile, in either case, will de- 
pend upon the velocity with which it is thrown. In 
each case the body will begin to move in the line of di- 
rection in which it is projected, but it will soon be de- 
flected from that line towards the earth. It will how- 
ever continue nearer to the line of projection as the ve- 

Fig. 29. 




locity of projection is greater. ^ Thus let AB (Fig. 29,) 



133. When a cannon ball is fired with different velocities, 
when is its motion nearest to the line of projection ? 



MOTION IN AN ELLIPTICAL ORBIT. 



105 



perpendicular to AC represent the line of projection. 
The body will, in ever)?- case, commence its motion in 
the hne AB, which will therefore be the tangent to the 
curve it describes ; but if it be thrown with a small ve- 
locity, it will soon depart from the tangent, describing 
the line AD ; with a greater velocity it will describe a 
curve nearer to the tangent, as AE ; and with a still 
greater velocity it will describe the curve AF. 

134. In figure 30, suppose the planet to have passed 
the point C with so small a velocity, that the attraction 
of the sun bends its path very much, and causes it im- 
mediately to begin to approach towards the sun ; the 
sun's attraction will increase its velocity as it moves 
through D, E, and F. For the sun's attractive force on 




the planet, when at D, is acting in the direction DS, 
and, on account of the small inclination of DE to DS, 
the force acting in the Hne DS helps the planet forward 
in the path DE, and thus increases its velocity. In like 
manner, the velocity of the planet will be continually 
increasing as it passes through E, and F ; and though 



134. Explain the motion of a planet in an elliptical orbit, 
from figure 30. 



106 UNIVERSAL GRAVITATION. 

the attractive force, on account of the planet's nearness, 
is much increased, and tends therefore to make the 
orbit more curved, yet the velocity is also so much in- 
creased that the orbit is not more curved than before. 
The same increase of velocity occasioned by the planet's 
approach to the sun, produces a greater increase of cen- 
trifugal force which carries it off again. We may see 
also why, when the planet has reached the most distant 
parts of its orbit, it does not entirely fly off*, and never 
return to the sun. For when the planet passes along 
H, K, A, the sun's attraction retards the planet, just as 
gravity retards a ball rolled up hill ; and when it has 
reached C, its velocity is very small, and the attraction 
at the center of force causes a great deflection from the 
tangent, sufficient to give its orbit a great curvature, 
and the planet turns about, returns to the sun, and goes 
over the same orbit again. As the planet recedes from 
the sun, its centrifugal force diminishes faster than the 
force of gravity, so that the latter finally preponderates. 

135. We may imitate the motion of a body in its orbit 
by suspending a small ball from the ceiHng by a long string. 
The ball being drawn out of its place of rest, (which is 
directly under the point of suspension,) it will tend con- 
stantly towards the same place by a force which corres- 
ponds to the force of attraction of a central body. If 
an assistant stands under the point of suspension, his 
head occupying the place of the ball when at rest, the 
ball may be made to revolve about his head as the earth 
or any planet revolves about the sun. By projecting the 
ball in different directions, and with different degrees of 
velocity, we may make it describe diflierent orbits, ex- 
emplifying principles which have been explained in the 
foregoing articles. 



135, How may we imitate the motion of a body in its or- 
bit 1 How may we make the ball describe diff*erent orbits ? 



PRECESSION OF THE EQUINOXES. 107 

PRECESSION OF THE EQUINOXES. 

136. The Precession of the equinoxes, is <r ilnw 

but continual shifting of the equinoctial points J^'' r 4CU& 
to west, ■ 

Suppose that we mark the exact place in the h^-^vens 
where, during the present year, the sun crosses the e>^^n^ 
tor, and that this point is close to a certain star ; ne/t- 
year the sun will cross the equator a little way west- 
ward of that star, and thus every year a little farther west- 
w^ard, so that in a long course of ages, the place of the 
equinox will occupy successively every part of the eclip- 
tic, until we come round to the same star again. As, 
therefore, the sun, revolving from w^est to east in his ap- 
parent orbit, comes round towards the point where it 
left the equinox, it meets the equinox before it reaches 
that point. The appearance is as though the equinox 
goes forward to meet the sun, and hence the phenome- 
non is called the Precession of the Equinoxes, and the 
fact is expressed by saying that the equinoxes retrograde 
on the ecliptic, until the line of the equinoxes makes a 
complete revolution from east to west. The equator is 
conceived as sliding westward on the ecliptic, always 
preserving the same inclination to it, as a ring placed at 
a small angle with another of nearly the same size, 
which remains fixed, may be slid quite around it, giving 
a corresponding motion to the two points of intersec- 
tion. It must be observed, however, that this mode of 
conceiving of the precession of the equinoxes is purely 
imaginary, and is employed merely for the convenience 
of representation. 

137. The amount of precession annually is 50. "1 ; 
whence, since there are 3600^^ in a decree, and 360° in 



136. Precession if the Equinoxes. — Define it. If the sun. 
crosses the equator uear a certain star this year, where will it 
cross it next year ? Why is the fact called the precession of 
the equinoxes ? How is the equator conceived as moving 
with regard to the ecliptic ? 



108 UNIVERSAL GRAVITATION. 

the whole circumference, and consequently, 1296000", 
this sum divided by 50.1 gives 25868 years for the pe- 
riod of a complete revolution of the equinoxes. 

138. Suppose now we fix to the center of each of the 
two rings, (Art. 136,) a wire representing its axis, one 
corresponding to the axis of the ecliptic, the other to 
that of the equator, the extremity of each being the pole 
of its circle. As the ring denoting the equator turns 
found on the ecliptic, which with its axis remains fixed, 
it is easy to conceive that the axis of the equator re- 
volves around that of the ecliptic, and the pole of the 
equator around the pole of the ecliptic, and constantly at 
a distance equal to the inclination of the two circles. To 
transfer our conceptions to the celestial sphere, we may 
easily see that the axis of the diurnal sphere, (that of 
the earth produced. Art. 15,) would not have its pole 
constantly in the same place among the stars, but that 
this pole would perform a slow revolution around the 
pole of the ecliptic from east to west, completing the cir- 
cuit in about 26,000 years. Hence the star which we 
now call the pole star, has not always enjoyed that dis- 
tinction, nor will it always enjoy it hereafter. When 
the earliest catalogues of the stars were made, this star 
was 12° from the pole. It is now 1° 33', and will ap- 
proach still nearer ; or to speak more accurately, the pole 
will come still nearer to this star, after which it will 
leave it, and successively pass by others. In about 
13,000 years, the bright star « Lyrae, which lies on the 
circle of revolution opposite to the present pole star, 



137. What is the amount of precession annually? In what 
time will the equinoxes perform a complete revolution ? 

138. Illustrate the precession of the equinoxes by an appa- 
ratus of wires. How is the pole of the earth situated with 
respect to the stars at different times? Has the present pole 
star always been such ? What will be the pole star 13,000 
years hence ? Will this cause affect the elevation of the 
north pole above the horizon ? 



PRECESSION OF THE EQUINOXES. 109 

will be within 5° of the pole, and will constitute the 
Pole Star. As « Lyrse now passes near our zenith, the 
learner might suppose that the change of position of the 
pole among the stars, would be attended with a change 
of altitude of the north pole above the horizon. This 
mistaken idea is one of the many misapprehensions 
which result from the habit of considering the horizon 
as a fixed circle in space. However the pole might 
shift its position in space, we should still be at the 
same distance from it, and our horizon would always 
reach the same distance beyond it. 

139. The time occupied hy the sun in passing from 
the equinoctial point round to the same point again, is 
called the tropical year. As the sun does not perform 
a complete revolution in this interval but falls short of it 
50." 1, the tropical year is shorter than the sidereal by 
20m. 20s. in mean solar time, this being the time of de- 
scribing an arc of SO.'^l in the annual revolution.* The 
changes produced by the precession of the equinoxes in 
the apparent places of the circumpolar stars, have led to 
some interesting results in chronology. In consequence 
of the retrograde motion of the equinoctial points, the 
signs of the ecliptic, do not correspond at present to 
the constellations which bear the same names, but lie 
about one whole sign or 30^ westward of them. Thus, 
that division of the ecliptic which is called the sign 
Taurus, lies in the constellation Aries, and the sign 
Gemini in the constellation Taurus. Undoubtedly how- 
ever when the ecliptic was thus first divided, and the 
divisions named, the several constellations lay in the re- 
spective divisions which bear their names. How long 
is it, then, since our zodiac was formed ? 



139. Define the tropical year. How much shorter is the 
tropical than the sidereal year ? How has the precession of the 
equinoxes been applied in Chronology ? 



59' 8/'3 : 24h. : : 50/a : 20m. 209. 
10 



110 THE MOON. 

50."1 : 1 year: :30°(=r 108000") : 2155.6 years. 
The result indicates that the present divisions of the 
zodiac, were made soon after the estabUshment of the 
Alexandrian school of astronomy. 



CHAPTER IV. 

OF THE MOON PHASES REVOLUTIONS. 

140. Next to the Sun the Moon naturally claims our 
attention. She is an attendant or satellite to the earth, 
around which she revolves at the distance of nearly 
240,000 miles, or more exactly 238,545 miles. Her 
angular diameter is about half a degree, and her real diam- 
eter 2160 miles. She is therefore a comparatively small 
body, being only one forty-ninth part as large as the 
earth. 

The moon shines by reflected light borrowed from 
the sun, and when full exhibits a disk of silvery bright- 
ness, diversified by extensive portions partially shaded. 
These dusky spots are generally said to be land, and the 
brighter parts water ; but astronomers tell us that if ei- 
ther are water, it must be the darker portions. Land by 
scattering the rays of the sun's light would appear more 
luminous than the ocean which reflects the light like a 
mirror. By the aid of the telescope, we see undoubted 
signs of a varied surface, in some parts composed of ex- 
tensive tracts of level country, and in others exceedingly 
broken by mountains and valleys. 

141. The line which separates the enlightened from 
the dark portions of the moon's disk, is called the Ter- 



140. The Moon. — What relation has the moon to the earth ? 
State her distance, diameter and bulk. Is her light direct or 
reflected ? What are the dark places in the moon generally un- 
derstood to be ? Why would water appear darker than land ? 
What does the telescope reveal to us respecting the moon ? 



LUNAR GEOGRAPHY. Ill 

minator. (See Frontispiece.) As the terminator traver- 
ses the disk from new to full moon, it appears through the 
telescope exceedingly broken in some parts, but smooth 
in others, indicating that portions of the lunar surface are 
uneven while others are level. The broken regions ap- 
pear brighter than the smooth tracts. The latter have 
been taken for seas, but it is supposed with more prob- 
ability that they are extensive plains, since they are still 
too uneven for the perfect level assumed by bodies of 
water. That there are mountains in the moon, is known 
by several distinct indications. First, when the moon 
is increasing, certain spots are illuminated sooner than 
the neighboring places, appearing like bright points be- 
yond the terminator, within the dark part of the disk, 
in the same manner as the tops of mountains on the 
earth are tipped with the light of the sun, in the morn- 
ing, while the regions below are still dark. Secondly, 
after the terminator has passed over them, they project 
shadows upon the illuminated part of the disk, always 
opposite to the sun, corresponding in shape to the form 
of the mountain, and undergoing changes in length from 
night to night, according as the sun shines upon that 
part of the moon more or less obHquely. Many indi- 
vidual mountains rise to a great height in the midst of 
plains, and there are several very remarkable mountain- 
ous groups, extending from a common center in long 
chains. 

142. That there are also valleys in the moon, is 
equally evident. The valleys are known to be truly 
such, particularly by the manner in which the hght of 
the sun falls upon them, illuminating the part opposite 
to the sun while the part adjacent is dark, as is the case 
when the light of a lamp shines obHquely into a china 



141 . Define the terminator. What do we learn from its rug- 
ged appearance ? State the proofs of mountains in the moon. 

1 42. State the proofs of valleys in the moon. When is the 
best time foi viewing the mountains and valleys of the moon. 



112 THE MOON. 

cup. These valleys are often remarkably regular, and 
some of them almost perfect circles. In several instan- 
ces, a circular chain of mountains surrounds an exten- 
sive valley, which appears nearly level, except that a 
sharp mountain sometimes rises from the center. The 
best time for observing these appearances is near the 
first quarter of the moon, when half the disk is en- 
lightened ;* but in studying the lunar geography, it is 
expedient to observe the moon every evening from new 
to full, or rather through her entire series of changes. 

143. The various places on the moon's disk have re- 
ceived appropriate names. The dusky regions, being 
formerly supposed to be seas, w^ere named accordingly ; 
and other remarkable places have each two names, one 
derived from some well known spot on the earth, and 
the other from some distinguished personage. Thus 
the same bright spot on the surface of the moon is 
called Mount Sinai or Tycho, and another. Mount Et- 
na or Copernicus. The names of individuals, how- 
ever, are more used than the others. The frontispiece 
exhibits the telescopic appearance of the full moon. A 
few of the most remarkable points have the following 
names, corresponding to the numbers and letters on the 
map. (See Frontispiece.) 

1. Tycho, A. Mare Humorum, 

2. Kepler, B. Mare Nubium, 

3. Copernicus, C. Mare Imbrium, 

4. Aristarchus, D. Mare Nectaris, 

5. Helicon, E. Mare Tranquilitatis, 

6. Eratosthenes, F. Mare Serenitatis, 

7. Plato, G. Mare Fecunditatis, 

8. Archimedes, H. Mare Crisium. 

9. Eudoxus, 
10. Aristotle. 



* It is earnestly recommended to the student of astronomy, to exam- 
ine the moon repeatedly with the best telescope he can command, using 
low powers at first, for the sake of a better light. 



LUNAR GEOGRAPHY. 113 

The frontispiece represents the appearance of the 
moon in the telescope when full and when five days 
old. In the latter cut, the learner will remark the rough, 
rugged appearance of the terminator ; the illuminated 
points beyond the terminator within the dark part of the 
moon, which are the tops of mountains ; and the nu- 
merous circular spaces, which exhibit valleys or caverns 
surrounded by mountainous chains. Those circles which 
are near the terminator into which the sun's light shines 
very obliquely, cast deep shadow^s on the sides opposite 
the sun. Those more remote from the terminator, and 
farther within the illum.inated part of the moon, into 
which the sun shines more directly, have a greater por- 
tion illuminated, with shorter shadows ; and those which 
lie near the edge of the moon, most distant from the ter- 
minator, are of an oval figure, being presented obliquely 
to the eye. 

144. The heights of the lunar mountains, and the 
depths of the valleys, can be estimated with a considera- 
ble degree of accuracy. Some of the mountains are as 
high as five miles, and the valleys in some instances 
are four miles deep. Hence it is inferred that the sur- 
face of the moon is more broken and irregular than that 
of the earth, its mountains being higher and its valleys 
deeper in proportion to its magnitude than that of the 
earth. The lunar mountains in general, exhibit an ar- 



143. How are places in the moon named ? Point out the 
most remarkable places on the map of the full moon. Point 
out the mountains, valleys, and craters, on the cut, which rep- 
resents the moon five days old. 

144. Specify the heights of some of the lunar mountains. 
Is the surface of the moon more or less broken than that of the 
earth ? Are the mountains like or unlike ours ? What is the 
first variety ? What is the shape of the insulated mountains? 
How can their heights be calculated ? W^hat is said of the 
second variet}^, the mountain ranges ? What is said of the 
circular ranges ? What is said of the central mountains 1 

10* 



114 THE MOON. 

rangement and an aspect very different from the moun- 
tain scenery of our globe. They may be arranged un- 
der the four following varieties. 

First, Insulated Mountains, which rise from plains 
nearly level, shaped like a sugar loaf, which may be 
supposed to present an appearance somewhat similar to 
Mount Etna, or the Peak of Teneriffe. The shadows 
of these mountains, in certain phases of the moon, are 
as distinctly perceived, as the shadow of an upright staff, 
when placed opposite to the sun ; and these heights can 
be calculated from the length of their shadows. Some 
of these mountains being elevated in the midst of exten- 
sive plains, would present to a spectator on their sum- 
mits, magnificent views of the surrounding regions. 

Secondly, Mountain Ranges, extending in length two 
or three hundred miles. These ranges bear a distant re- 
semblance to our Alps, Appenines, and Andes ; but they 
are much less in extent. Some of them appear very 
rugged and precipitous, and the highest ranges are in 
some places more than four miles in perpendicular alti- 
tude. In some instance^, they are nearly in a straight 
line from northeast to southwest, as in that range called 
the Appenines ; in other cases they assume the form of 
a semicircle or crescent. 

Thirdly, Circular Ranges, which appear on almost 
every part of the moon's surface, particularly in its south- 
ern regions. This is one grand peculiarity of the lunar 
ranges, to which we have nothing similar on the earth. 
A plain, and sometimes a large cavity, is surrounded 
with a circular ridge of mountains, which encompasses 
it like a mighty rampart. These annular ridges and 
plains are of all dimensions, from a mile to forty or fifty 
miles in diameter, and are to be seen in great numbers 
over every region of the moon's surface ; they are most 
conspicuous, however, near the upper and lower limbs 
about the time of half moon. 

The mountains which form these circular ridges are 
of different elevations, from one fifth of a mile to three 
and a half miles, and their shadows cover one half of 
the plain at the base. These plains are sometimes on 



LUNAR GEOGRAPHY. 115 

a level with the general surface of the moon, and in 
other cases they are sunk a mile or more below the level 
of the ground, which surrounds the exterior circle of the 
mountains. 

Fourthly, Central Mountains, or those which are 
placed in the middle of circular plains. In many of the 
plains and cavities surrounded by circular ranges of 
mountains there stands a single insulated mountain, 
which rises from the center of the plain, and whose 
shadow sometimes extends in the form of a pyramid 
half across the plain or more to the opposite ridges. 
These central mountains are generally from half a mile 
to a mile and a half in perpendicular altitude. In some 
instances they have two and sometimes three different 
tops, whose shadows can be easily distinguished from 
each other. Sometimes they are situated towards one 
side of the plain or cavity, but, in the great majority 
of instances, their position is nearly or exactly central. 
The lengths of their bases vary from five to about fifteen 
or sixteen miles. 

145. The Lunar Caverns form a very pecuHar and 
prominent feature of the moon's surface, and are to 
be seen throughout almost every region, but are most 
numerous in the southwest part of the moon. Nearly a 
hundred of them, great and small, may be distinguished 
in that quarter. They are all nearly of a circular shape, 
and appear like a very shallow egg-cup. The smaller 
cavities appear within almost like a hollow cone, with 
the sides tapering towards the center ; but the larger 
ones have for the most part, flat bottoms, from the cen- 
ter of which there frequently rises a small steep conical 
hill, which gives them a resemblance to the circular 
ridges and central mountains before described. In some 
instances their margins are level with the general sur- 
face of the moon, but in most cases they are encircled 



145. Lunar Caverns. — What is said of their number, shape 
and appearanres ? 



116 THE MOON. 

with a high annular ridge of mountains, marked with 
lofty peaks. Some of the larger of these cavities con 
tain smaller cavities of the same kind and form, particu- 
larly in their sides. The mountainous ridges which sur- 
round these cavities, reflect the greatest quantity of 
light ; and hence that region ^f the moon in which they 
abound, appears brighter than any other. From their 
lying in every possible direction, they appear at and 
near the time of full moon, like a number of brilliant 
streaks or radiations. These' radiations appear to con- 
verge towards a large brilliant spot, surrounded by a 
faint shade, near the lower part of the moon which is 
named Tycho, (Frontispiece, 1,) which may be easily dis- 
tinguished even by a small telescope. The spots named 
Kepler and Copernicus, are each composed of a central 
spot with luminous radiations.* 

146. Dr. Herschel is supposed also to have obtained 
decisive evidence of the existence of volcanoes in the 
moon, not only from the light afforded by their fires, 
but also from the formation of new mountains by the 
accumulation of matter where fires had been seen to 
exist, and which remained after the fires were extinct. 

147. Some indications of an atmosphere about the 
moon have been obtained, the most decisive of which 
are derived from appearances of twilight, a phenomenon 
that implies the presence of an atmosphere. Similar in- 
dications have been detected, it is supposed, in eclipses 
of the sun, denoting a transparent refracting medium 
encompassing the moon. 



146. Volcanoes. — What proofs are there of their having ex- 
isted in the moon ? 

147. What evidence is there of a lunar atmosphere ? 



* The foregoinsj accurate description of the lunar mountains and cay. 
ems is from " Dick's Celestial Scenery." 



LUNAR GEOGRAPHT?. 117 

148. It has been a question with astronomers, whether 
there is water in the moon ? The general opinion is 
that there is none. If there were any, we should ex- 
pect to see clouds ; or at least we should expect to find 
the face of the moon occasionally obscured by clouds ; 
but this is not the case, since the spots on the moon's 
disk, when our sky is clear, are always in full view. 
The deep caverns, moreover, seen in those dusky spots 
which were supposed to be seas, are unfavorable to the 
supposition, that they are surrounded by water ; and the 
terminator when it passes over these places is, as already 
remarked, too uneven to permit us to suppose that these 
tracts are seas. 

149. The improbability of our ever identifying arti- 
ficial structures in the moon, may be inferred from the 

fact that a line one mile in length in the moon subtends 
an angle at the eye of only about one second. If, there- 
fore, works of art were to have a sufficient horizontal 
extent to become visible, they can hardly be supposed 
to attain the necessary elevation, when we reflect that 
the height of the great pyramid of Egypt is less than 
the sixth part of a mile. Still less probable is it that we 
shall ever discover any inhabitants in the moon. The 
greatest magnifying power that has ever been applied 
with distinctness, to the moon, does not much exceed a 
thousand times, bringing the moon apparently a thou- 
sand times nearer to us than w^hen seen by the naked 
eye. But this implies a distance still of 240 miles ; and 



148. Is there water in the moon ? What proofs are there 
to the contrary ? 

149. Is it probable that artificial structures in the moon will 
ever be identified ? How high must they he, in order to be 
seen distinct from the surface ? Is it probable that we shall 
ever be able to recognize inhabitants in the moon ? What is 
the greatest magnifying power of the telescope that has ever 
been applied to the moon ? If we could magnify the moon 
1 0,000 times what would still be her apparent distance ? What 
inherent difiSculty is there in employing very great magnifiers ? 



118 THE MOON. 

could we magnify the moon ten thousand times, her ap- 
parent distance would still be twenty-four miles, a dis- 
tance too great to distinguish living beings. Moreover, 
when we use such high magnifiers in the telescope, our 
field of view is necessarily exceedingly small, so that it 
would be a mere point that we could view at a time. 
This difficulty is inherent in the very nature of tele- 
scopes, namely, that the field of view is reduced as the 
magnifying power is increased ; and we magnify the 
vapors and the undulations of the atmosphere, as well 
as the moon, and by this means impair the medium so 
much that we should not be able to see anything with 
distinctness. It is only to such minute objects as a star, 
that very high powers of the telescope can ever be ap- 
plied. 

150. Some writers, however, suppose that possibly 
we may trace indications of lunar inhabitants in their 
works, and that they may, in like manner, recognize the 
existence of the inhabitants of our planet. An author 
who has reflected much on subjects of this kind, rea- 
sons as follows : A navigator who approaches within a 
certain distance of a small island, although he perceives 
no human being upon it, can judge with certainty, that 
it is inhabited, if he perceives human habitations, villa- 
ges, cornfields, or other traces of cultivation. In like 
manner, if we could perceive changes or operations in 
the moon, which could be traced to the agency of intel- 
ligent beings, we should then obtain satisfactory evi- 
dence, that such beings exist on that planet ; and it is 
thought possible that such operations may be traced. 
A telescope which magnifies 1200 times, will enable us 
to perceive, as a visible point on the surface of the moon, 
an object whose diameter is only about 300 feet. Such 



150. What have some writers supposed with respect to the 
probability of our tracing marks of living beings on the moon ? 
How is it proposed to have the moon examined for this pur- 
pose ? 



LUNAR GEOGRAPHY. 119 

an object is not larger than many of our public edifices ; 
and, therefore, were any such edifices rearing in the 
moon, or were a town or city extending its boundaries, 
or were operations of this description carrying on in a 
district where no such edifices had previously been 
erected, such objects and operations might probably be 
detected by a minute inspection. Were a multitude of 
living creatures moving from place to place in a body, 
or were they even encamping in an extensive plain, like 
a large army, or like a tribe of Arabs in the desert, and 
afterwards removing, it is possible that such changes 
might be traced by the diflference of shade or color, 
which such movements would produce. In order to de- 
tect such minute objects and operations, it would be 
requisite that the surface of the moon should be distrib- 
uted among at least a hundred astronomers, each having 
a spot or two allotted to him, as the object of his more 
particular investigation, and that the observations be 
continued for a period of at least thirty or forty years, 
during which time certain changes would probably be 
perceived, arising either from physical causes, or from 
the operations of living agents.* 

151. It has sometimes been a subject of speculation, 
whether it might be possible, by any symbols, to cor- 
respond with the inhabitants of the moon. It has been 
suggested, that if some vast geometrical figure, as a 
square or a triangle, were erected on the plains of Siberia, 
it might be recognized by the lunarians, and answered 
by some corresponding signal. Some geometrical figure 
would be peculiarly appropriate for such a telegraphic 
commerce with the inhabitants of another sphere, since 
these are simple ideas common to all minds. 



151. How is it proposed to carry on a telegraphic communi- 
cation with the lunarians ? 



* Dick's Celestial Scenery, Ch. lY, 



120 THE MOON. 

PHASES OF THE MOON. 

152. The changes of the moon, commonly called her 
Phases, arise from different portions of her illuminated 
side being turned towards the earth at different times. 
When the moon is first seen after the setting sun, her 
form is that of a bright crescent, on the side of the disk 
next to the sun, while the other portions of the disk 
shine with a feeble light, reflected to the moon from the 
earth. Every night we observe the moon to be farther 
and farther eastward of the sun, and at the same time 
the crescent enlarges, until, when the moon has reached 
an elongation from the sun of 90°, half her visible disk 
is enlightened, and she is said to be in her first quarter. 
The terminator, or line which separates the illuminated 
from the dark part of the moon, is convex towards the 
sun from the new moon to the first quarter, and the 
moon is said to be horned. The extremities of the 
crescent are called cusps. At the first quarter, the ter- 
minator becomes a straight line, coinciding with a di- 
ameter of the disk ; but after passing this point, the ter- 
minator becomes concave towards the sun, bounding 
that side of the moon by an elliptical curve, when the 
moon is said to be gibbous. When the moon arrives at 
the distance of 180° from the sun, the entire circle is 
illuminated, and the moon is full. She is then in oppo- 
sition to the sun, rising about the time the sun sets. For 
a week after the full, the moon appears gibbous again, 
until, having arrived within 90° of the sun, she re- 
sumes the same form as at the first quarter, being then 
at her third quarter. From this time until new moon, 
she exhibits again the form of a crescent before the ri- 
sing sun, until, approaching her conjuTWtion with the 



152. Phases of the Moon. — Whence do they rise ? State 
the successive appearances of the moon from new to full. In 
what parts of her revolution is she horned, and in what parts 
gibbous ? When is she said to be in conjunction, and when in 
opposition ? What are the syzigies, quadratures, and octants 1 
Define the circle of illumination, and the ciicle of the disk. 



PHASES. 121 

sun, her narrow thread of Hght is lost in the solar blaze ; 
and finally, at the moment of passing the sun, the dark 
side is wholly turned towards us, and for some time we 
lose sight of the moon. 

The two points in the orbit corresponding to new and 
full moon respectively, are called by the common name 
of syzigies ; those which are 90° from the sun are 
called quadratures ; and the points half way between 
the syzigies and quadratures are called octants. The 
circle which divides the enlightened from the unen- 
lightened hemisphere of the moon, is called the circle of 
illumination: that which divides the hemisphere that 
is turned towards us from the hemisphere that is turn- 
ed from us, is called the circle of the disk. 

153. As the moon is an opake body of a spherical 
figure, and borrows her hght from the sun, it is obvious 

Fig. 31 




that that half only which is towards the sun can be il- 
luminated. More or less of this side is turned towards 
the earth, according as the moon is at a greater or less 
elongation from the sun. The reason of the different 
phases will be best understood from a diagram. There- 
fore let T (Fig. 31,) represent the earth, and S the sun. 
11 



122 THE MOON. 

Let A, B, C, &c. be successive positions of the mooa. 
At A the entire dark side of the moon being turned to- 
wards the earth, the disk would be wholly invisible. At 
B, the circle of the disk cuts of a small part of the en- 
lightened hemisphere, which appears in the heavens at 
b, under the form of a crescent. At C, the first quarter, 
the circle of the disk cuts off half the enlightened hem- 
isphere, and a half moon is seen at c. In like manner it 
will be seen that the appearances presented at D, E, F, 
&c. must be those represented at d, e, f. If a round 
body, as an apple, suspended by a string, be carried 
around a lamp, the eye remaining fixed opposite to it at 
the same level, the various phases of the moon will be 
exhibited. 

REVOLUTIONS OF THE MOON. 

154. The moon revolves around the earth from west 
to east, making the entire circuit of the heavens in about 
27i dai/s. 

The period of the moon's revolution from any point 
in the heavens round to the same point again, is called 
a month. A sidereal month is the time of the moon's 
passing from any star, until it returns to the same star 
again. A synodical month, so called from two Greek 
words implying that at the end of this period the two 
bodies (the sun and moon) come together, is the time 
from one conjunction or new moon to another. The 
synodical month is about 29j days, or more exactly, 
29d. 12h. 44m. 2s.8 =29.53 days. The sidereal month 
is about two days shorter, being 27d. 7h. 43m. lls.5. 
or 27.32 days. As the sun and moon are both revolv- 
ing in the same direction, and the sun is moving nearly 



153. How much of the moon is illuminated at once? Ex- 
plain the phases of the moon from figure 31. 

154. Define a month. Define a sidereal month. Also a sy- 
nodical month. Why so called ? What is the length of the 
synodical month ? Also of the sidereal month ? What is the 
moon's daily motion ? 



REVOLUTIONS. 123 

a degree a day, during the 27 days of the mov^fi's revo- 
lution, the sun must have moved 27^. Now since the 
moon passes over 360° in 27.32 days, her daily motion 
must be 13° 17'. It must therefore evidently take about 
two days for the moon to overtake the sun. 

155. The moorCs orhit is inclined to the ecliptic in an 
angle of about 5° (5° 8' 48".) The moon crosses the 
echptic in two opposite points called her nodes. That 
which the moon crosses from south to north, is called 
her ascending node, that w^hich she crosses from north 
to south, her descending node. The moon, therefore, is 
never seen far from the ecliptic, but the path she pur- 
sues through the skies, is very nearly the same as that 
of the sun in his annular revolution around the earth. 

156. The moon, at the same age, crosses the meridian 
at different altitudes at different seasons of the year ; and 
accordingly it is said to run sometimes high and some- 
times low. The full moon, for example, will appear 
much farther in the south when on the meridian at one 
period of the year than at another. The reason of this 
may be explained as follow^s. When the sun is in the 
part of the ecliptic south of the equator, the earth and 
of course the moon, which always keeps near to the 
earth, is in the part north of the equator. At such 
times, therefore, the new moons, which are always 
seen in the part of the heavens where the sun is, will 
run far south, while the full moons, which are always in 
the opposite part of the heavens from the sun, will run 
high. Such is the case during the winter months ; but, 



1 55. How much is the moon's orbit inclined to the ecliptic ? 
Define the nodes. What is the ascending and Avhat the de- 
scending node ? 

1 56. Why does the moon run high and low 1 At what sea- 
son of the year are the full moons longest above the horizon ? 
Explain how this operates favorably to those who are near 
the pole. 



124 THE MOON. 

in the summer, when the sun is towards the northern 
tropic and the earth towards the soirthern, the new 
moons run high and the full moons low. This arrange- 
ment gives us a great advantage in respect to the amount 
of light received from the moon ; since the full moon 
is longest above the horizon during the long nights of 
winter, when her presence is most needed. This cir- 
cumstance is especially favorable to the inhabitants of 
the polar regions, the moon, w^hen full, traversing that 
part of her orbit which lies north of the equator, and of 
course above the horizon of the north pole, and traver- 
sing the portion that lies south of the equator, and be- 
low the polar horizon, when new. During the polar 
winter, therefore, the moon, during her second and third 
quarters, when she gives most light, is commonly above 
the horizon, while the sun is absent ; whereas, during 
summer, while the sun is present and the light is not 
needed, during her second and third quarters, she is be- 
low the horizon. 

157. About the time of the autumnal equinox, the 
moon when near the full, rises about sunset for a num- 
ber of nights in succession ; and as this is, in England, 
the period of harvest, the phenomenon is called the 
Harvest Moon. To understand the reason of this, since 
the moon is never far from the ecliptic, we will suppose 
her progress to be in the ecliptic. If the moon moved 
in the equator, then, since this great circle is at right 
angles to the axis of the earth, all parts of it, as the 
earth revolves, cut the horizon at the same constant 
angle. But the moon's orbit, or the ecliptic, which is 
here taken to represent it, being oblique to the equator, 
cuts the horizon at different angles in different parts, as 
will easily be seen by reference to an artificial globe. 
When the first of Aries, or vernal equinox, is in the 



157. Why is the harvest moon so called ? Explain its cause. 
How is the moon's orbit inclined to the horizon at different 
times ? 



REVOLUTIONS. 125 

eastern horizon, it will be seen that the ecliptic, (and 
consequently the moon's orbit,) makes its least angle 
with the horizon. Now, at the autumnal equinox, the 
sun being in Libra, the moon at the full, when she is 
always opposite to the sun, is in Aries, and rises when 
the sun sets. On the following evening, although she 
has advanced in her orbit about 13^, yet her progress be- 
ing obHque to the horizon, and at a small angle with it, 
she will be found at this time but a little way below the 
horizon, compared with the point where she was at sun- 
set the preceding evening. She therefore rises but little 
later, and so for a week only a little later each evening 
than she did the preceding night. 

158. The moon turns on its axis in the same time in 
which it revolves around the earth. 

This is known by the moon's always keeping nearly 
the same face towards us, as is indicated by the tele 
scope, which could not happen unless her revolution on 
her axis kept pace with her motion in her orbit. Thus 
it will be seen by inspecting figure 22, that the earth 
turns diiferent faces tov/ards the sun at different times ; 
and if a ball having one hemisphere white and the 
other black be carried around a lamp, it will easily be 
seen that it cannot present the same face constantly to- 
wards the lamp unless it turns once on its axis while 
performing its revolution. The same thing will be ob- 
served when a man walks around a tree, keeping his face 
constantly towards it. Since however the motion of 
the moon on its axis is uniform, while the motion in its 
orbit is unequal, the moon does in fact reveal to us a lit- 
tle sometimes of one side and sometimes of the other. 
Thus when the ball above mentioned is placed before 
the eye with its light side towards us, on carrying it 
round, if it is moved faster than it is turned on its axis, 



158. In what time does the moon turn on its axis ? Illus- 
trate by the motion of a ball around a lamp. Is the same side 
of the moon alwavs turned exactly towards us ? 
II* 



126 THE MOON. 

a portion of the dark hemisphere is brought into view 
on one side ; or if it is moved forward slower than it is 
turned on its axis, a portion of the dark hemisphere 
comes into view on the other side. 

159. These appearances are called the moon's lihr^a- 
tions in longitude. The moon has also a libration in 
latitude, so called, because in one part of her revolution, 
more of the region around one of the poles comes into 
view, and in another part of the revolution, more of the 
region around the other pole ; w^hich gives the appear- 
ance of a tilting motion to the moon's axis. This has 
nearly the same cause w'ith that which occasions our 
change of seasons. The moon's axis being inclined to 
the plane of her orbit, and ahvays remaining parallel to 
itself, the circle which divides the visible from the in- 
visible part of the moon, will pass in such a way as to 
throw sometimes more of one pole into view, and some- 
times more of the other, as would be the case with the 
earth if seen from the sun. (See Fig. 22.) 

The moon exhibits another phenomenon of this kind 
called her diurnal libration, depending on the daily ro- 
tation of the spectator. She turns the same face to- 
wards the center of the earth only, whereas we view 
her from the surface. When she is on the meridian, we 
see her disk nearly as though we viewed it from the 
center of the earth, and hence in this situation it is sub- 
ject to little change ; but when near the horizon, our 
circle of vision takes in more of the upper limb than 
would be presented to a spectator at the center of the 
earth. Hence, from this cause, we see a portion of one 
limb while the moon is rising, w'hich is gradually lost 
sight of, and w^e see a portion of the opposite limb as 
the moon declines to the west. It will be remarked 
that neither of the foregoing changes implies any actual 
motion in the moon, but that each arises from a change 
of position in the spectator. 



159. Explain the librations in longitude. Ditto in latitude. 
Ditto the diurnal Ubrations. 



REVOLUTIONS. 127 

160. Since the succession of day and night depends 
on the revolution of a planet on its own axis, an inhab- 
itant of the moon would have but one day and one night 
during the whole lunar month of 29^ days. One of its 
days, therefore, is equal to nearly 15 of ours. So pro- 
tracted an exposure to the sun's rays, especially in the 
equatorial regions of the moon, must occasion an exces- 
sive accumulation of heat ; and so long an absence of 
the sun must occasion a corresponding degree of cold. 
Each day would be a wearisome summer ; each night a 
severe winter.* A spectator on the side of the moon 
which is opposite to us would never see the earth ; but 
one on the side next to us w^ould see the earth present- 
ing a gradual succession of changes during his long 
night of 360 hours. Soon after the earth's conjunction 
with the sun, he would have the light of the earth re- 
flected to him, presenting at first a crescent, but enlarg- 
ing as the earth approaches its opposition, to a great orb, 
13 times as large as the full moon appears to us, and af- 
fording nearly 13 times as much light. Our seas, our 
plains, our mountains, our volcanoes, and our clouds, 
w^ould produce very diversified appearances, as would 
the various parts of the earth brought successively into 
viev/ by its diurnal rotation. The earth w^hile in view 
to an inhabitant of the moon, would remain immovably 
fixed in the same part of the heavens. For being un- 
conscious of his own motion around the earth, as we are 
of our motion around the sun, the earth would seem to 
revolve around his own planet from w^est to east, just as 
the moon appears to us to revolve about the earth ; but, 
meanwhile, his rotation along with the moon on her 
axis, would cause the earth to have an apparent motion 



160. How many days would an inhabitant of the moon have 
in a lunar month ? What vicissitudes of temperature would 
occur in a single day ? Would a spectator on the side of the 
moon opposite to us, ever see the earth ? How would the earth 
appear to a spectator on the side of the moon next to us ? 

* Francoeur, Uranog. p. 91. 



128 THE MOON. 

westward at the same rate. The two motions, there- 
fore, would exactly balance each other, and the earth 
would appear all the while at rest. 

161. We have thus far contemplated the revolution 
of the moon around the earth as though the earth were 
at rest. But, in order to have just ideas respecting the 
moon's motions, we must recollect that the moon like- 
wise revolves along with the earth around the sun. It 
is sometimes said that the earth carries the moon along 
with her in her annual revolution. This language may 
convey an erroneous idea ; for the moon, as well as the 
earth, revolves around the sun under the influence of 
two forces, and would continue her motion around the 
sun were the earth removed out of the way. Indeed, 
the moon is attracted towards the sun 2\ times more 
than towards the earth, and would abandon the earth 
were not the latter also carried along with her by the 
same forces. So far as the sun acts equally on both 
bodies, their motion with respect to each other would 
not be disturbed. Because the gravity of the moon to- 
wards the sun is found to be greater, at the conjunction, 
than her gravity towards the earth, some have appre- 
hended that, if the doctrine of universal gravitation is 
true, the moon ought necessarily to abandon the earth. 
In order to understand the reason why it does not do 
thus, we must reflect, that when a body is revolving in 
its orbit under the action of the projectile force and 
gravity, whatever diminishes the force of gi'avity while 
that of projection remains the same, causes the body to 
approach nearer to the tangent of her orbit, and of course 
to recede from the center ; and whatever increases the 
amount of gravity carries the body towai'ds the center. 



161. Can it be said that the earth carries the moon around 
the sun ? How much more is the moon attracted towards the 
sun than towards the earth ? Why does not the moon abandon 
the earth ? When the sun acts equally on both bodies, does it 
disturb their relative places? How does the sun act upau 
these bodies at the conjunctions and oppositions ? 



REVOLUTIONS. 129 

Now, when the moon is in conjunction, her gravity to- 
wards the earth acts in opposition to that towards the 
sun, while her velocity remains too great to carry her, 
with what force remains, in a circle about the sun, and 
she therefore recedes from the sun, and commences her 
revolution around the earth. On arriving at the opposi- 
tion, the gravity of the earth conspires with that of the 
sun, and the moon's projectile force being less than that 
required to make her revolve in a circular orbit, when 
attracted towards the sun by the sum of these forces, she 
accordingly begins to approach the sun and descends 
again to the conjunction. 

162. The attraction of the sun, however, being every 
where greater than that of the earth, the actual path of 
the moon around the sun is every where concave to- 
wards the latter. Still the elliptical path of the moon 
around the earth, is to be conceived of in the same way 
as though both bodies were at rest with respect to the 
sun. Thus, while a steamboat is passing swiftly around 
an island, and a man is walking slowly around a post in 
the cabin, the line which he describes in space between 
the forward motion of the boat and his circular motion 
around the post, may be every where concave towards 
the island, while his path around the post will still be 
the same as though both were at rest. A nail in the rim 
of a coach wheel, will turn around the axis of the wheel, 
when the coach has a forward motion in the same man- 
ner as when the coach is at rest, although the line ac- 
tually described by the nail will be the resultant of both 
motions, and very different from either. 

163. We have hitherto regarded the moon as descri- 
bing a great circle on the face of the sky, such being the 



162. How is the moon's path in space with respect to the 
sun ? How is the elliptical path of the moon around the earth 
to be conceived of ? How is this illustrated by the motions of 
a man in a steamboat ? Also by the motions of a nail in the 
rim of a coach wheel ■? 



130 THE MOON. 

visible orbit as seen by projection. But, on more exact 
investigation, it is found that her orbit is not a circle, 
and that her motions are subject to very numerous ir- 
regularities. These will be best understood in connec- 
tion with the causes on which they depend. The law 
of universal gravitation has been applied with wonder- 
ful success to their investigation, and its results have 
conspired with those of long continued observation, to 
furnish the means of ascertaining with great exactness 
the place of the moon in the heavens at any given in- 
stant of time, past or future, and thus to enable astrono- 
mers to determine longitudes, to calculate eclipses, and 
to solve various other problems of the highest interest. 
A complete understanding of all the irregularities of the 
moon's motions, must be sought for in more extensive 
treatises of astronomy than the present ; but some gen- 
eral acquaintance with the subject, clear and intelligible 
as far as it goes, may be acquired by first gaining a dis- 
tinct idea of the mutual actions of the sun, the moon, 
and the earth. 

164. The irregularities of the moorCs motions^ are 
due chiefly to the disturbing injiuence of the sun, which 
operates in two ways ; first, by acting unequally on the 
earth and moon, and, secondly, by acting obliquely on 
the moon, on account of the inclination of her orbit to 
the ecliptic. 

If the sun acted equally on the earth and moon, and 
always in parallel lines, this action would serve only to 
restrain them in their annual motions round the sun, and 
would not affect their actions on each other, or their 
motions about their common center of gravity. In that 
case, if they were allowed to fall directly towards the 
sun, they would fall equally, and their respective situa- 
tions would not be aflected by their descending equally 
towards it. We might then conceive them as in a 
plane, every part of which being equally acted on by 



163. Are the motions of the moon regular or irregular ? By 
what general law are they explained ? 



REVOLUTIONS. 131 

the sun, the whole plane would descend towards the 
sun, but the respective motions of the earth and the 
moon in this plane, would be the same as if it were 
quiescent. Supposing then this plane and all in it, 
to have an annual motion imprinted on it, it would 
move regularly around the sun, while the earth and moon 
would move in it with respect to each other, as if the 
plane were at rest, without any irregularities. But be- 
cause the moon is nearer the sun in one half of her orbit 
than the earth is, and in the other half of her orbit is at 
a greater distance than the earth from the sun, while the 
power of gravity is always greater at a less distance ; it 
follows, that in one half of her orbit the moon is more 
attracted than the earth towards the sun, and in the other 
half less attracted than the earth. The excess of the 
attraction, in the first case, and the defect in the second, 
constitutes a disturbing force, to which we may add an- 
other, namely, that arising from the oblique action of the 
solar force, since this action is not directed in parallel 
lines, but in lines that meet in the center of the sun. 

165. To see the effects of this process, let us suppose 
that the projectile motions of the earth and moon were 
destroyed, and that they were allowed to fall freely to- 
wards the sun. If the moon was in conjunction with 
the sun, or in that part of her orbit which is nearest to 
him, the moon would be more attracted than the earth, 
and fall with greater velocity towards the sun ; so that 
the distance of the moon from the earth would be in- 
creased in the fall. If the moon was in opposition, or 



164. To what cause are the inequalities of the moons mo- 
tions chiefly due ? If the sun acted equally on the earth and 
moon, and in parallel lines, would it disturb their motions 1 If 
allowed to fall towards the sun, how would they fall 1 How 
might we conceive them as situated in a plane ? When is the 
moon more attracted than the earth % When is the earth more 
attracted than the moon 1 What constitutes the disturbing face. 

165. Trace the effects of the sun, if the projectile force were 
destroved, at conjunction, at opposition, and at quadrature. 



132 THE MOON. 

in the part of her orbit which is farthest from the sun, 
she would be less attracted than the earth by the sun, 
and would fall with a less velocity towards the sun, and 
would be left behind ; so that the distance of the moon 
from the earth would be increased in this case also. If 
the moon was in one of the quarters, then the earth and 
moon being both attracted towards the center of the 
sun, they would both descend directly towards that cen- 
ter, and by approaching it, they would necessarily at 
the same time approach each other, and in this case their 
distance from each other would be diminished. Now 
whenever the action of the sun would increase their dis- 
tance, if they were allowed to fall towards the sun, 
then the sun's action, by endeavouring to separate them, 
diminishes their gravity to each other; whenever the 
sun's action would diminish the distance, then it in- 
creases their mutual gravitation. Hence, in the con- 
junction and opposition, that is, in the syzigies^ their 
gravity towards each other is diminished by the action 
of the sun, while in the quadratures it is increased. 
But it must be remembered that it is not the total action 
of the sun on them that disturbs their motions, but only 
that part of it which tends at one time to separate them, 
and at another time to bring them nearer together. The 
other and far greater part, has no other effect than to 
retain them in their annual course around the sun. 

166. The figure of the moorCs orbit is an ellipse, hav- 
ing the earth in one of the foci. 

The greatest and least distances of the moon from the 
earth, are nearly 64 and 56, the radius of the earth being 
taken for unity. Hence, taking the arithmetical mean, 
we find that the mean distance of the moon from the 



166. What is the figure of the moon's orbit ? What are the 
greatest and least distances of the moon from the earth ? De- 
fine the terms perigee and apogee. What numbers express the 
greatest and least distance of the sun from the earth ? How 
does the eccentricity of the lunar orbit compare with that of 
the solar ? 



I 



REVOLUTIONS. 133 

earth is very nearly 60 times the radius of the earth. 
The point in the moon's orbit nearest the earth, is 
called her perigee ; the point farthest from the earth, 
her apogee. 

The greatest and least distances of the sun are re- 
spectively as the numbers 32.583, and 31.5] 7. By com- 
paring this ratio with that of the distances of the moon, 
it will be seen that the latter vary much more than the 
former, and consequently that the lunar orbit is much 
more eccentric than the solar. The eccentricity of the 
moon's orbit is in fact -^ of its mean distance from the 
earth, while that of the earth is only ^ of its mean dis- 
tance from the sun, 

167. The mooiLS nodes constantly shift their positions 
in the ecliptic from east to west, at the rate of 19° ^b' per 
annum, returning to the same points in 18.6 years. 

Suppose the great circle of the ecliptic marked out on 
the face of the sky in a distinct line, and let us observe, 
at any given time, the exact point where the moon 
crosses this line, which we w'ill suppose to be close to a 
certain star ; then, on its next return to that part of the 
heavens, we shall find that it crosses the ecliptic sensi- 
bly to the w^estward of that star, and so on, farther and 
farther to the westw^ard every time it crosses the ecliptic 
at either node. This fact is expressed by saying that 
the nodes retrograde on the ecliptic, and that the line 
which joins them, or the line of the nodes, revolves frSn 
east to west. 

168. The period occupied by the sun in passing from 
one of the moon's nodes until it comes round to the 
same node again, is called the synodical revolution of the 
node. This period is shorter than the sidereal year, be- 
ing only about 346^ days. For since the node shifts its 



167. How do the moon's nodes shift their position ? In 
what time do they make a complete revolutin in the ecliptic ? 
Explain what is mean" by saying that the nodes retrogade. 
12 



134 THE MOON. 

place to the westward 19^ 35' per annum, the sun, in 
his annual revolution, comes to it so much before he 
completes his entire circuit ; and since the sun moves 
about a degree a day, the synodical revolution of the 
node is 365—19 = 346, or more exactly, 346.619851. 
The time from one new moon, or from one full moon, 
to another, is 29.5305887 days. Now 19 synodical rev- 
olutions of the nodes contain very nearly 223 of these 
periods. 

For 346.619851 x 19 = 6585.78. 
And 29.5305887x223 = 6585.32. 
Hence, if the sun and moon were to leave the moon's 
node together, after the sun had been round to the same 
node 19 times; the moon would have made very nearly 
223 conjunctions with the sun, and would therefore, at 
the end of this period meet at the same node, to repeat 
the same circuit. And since eclipses of the sun and 
moon depend upon the relative position of the sun, the 
moon, and node, these phenomena are repeated in nearly 
the same order, in each of those periods. Hence, this 
period, consisting of about 18 years and 10 days, under 
the name of the Saj^os, was used by the Chaldeans and 
other ancient nations in predicting echpses. 

169. The Metonic Cycle is not the same with the Sa- 
ros, but consists of 19 tropical years. During this pe- 
riod the moon makes very nearly 235 synodical revolu- 
tftns, and hence the new and full moons, if reckoned 
by periods of 19 years, recur at the same dates. If, for 
example, a new moon fell on the fiftieth day of one 
cycle, it would also fall on the fiftieth day of each suc- 



168. What is meant by the synodical revolution of the node ? 
How many new moons occur in 19 synodical revolutions of the 
node 1 Why was this period used in predicting eclipses ? What 
was it called ? 

169. What is the period of the Metonic Cycle ? How many 
conjunctions of the moon with the sun occur during this pe- 
riod ? What usct did the Athenians make of this lunar cycle ? 



REVOLUTIONS. 135 

ceeding cycle ; and, since the regulation of games, 
feasts, and fasts, has been made very extensively ac- 
cording to new or full moons, hence this lunar cycle has 
been much used both in ancient and modern times. 
The Athenians adopted it 433 years before the Christian 
era, for the regulation of their calendar, and had it in- 
scribed in letters of gold on the walls of the temple of 
Minerva. Hence the term Golden Number, which de- 
notes the year of the lunar cycle. 

170. The line of the apsides of the moon's orbit re- 
volves from west to east through her whole orbit in about 
nine years. 

If, in any revolution of the moon, we should accu- 
rately mark the place in the heavens where the moon 
comes to its perigee, (which would be known by the 
moon's apparent diameter being then greatest,) we should 
find, that at the next revolution, it would come to its 
perigee at a point a little farther eastw^ard than before, 
and so on at every revolution, until, after nine years, it 
would come to its perigee at nearly the same point as at 
first. This fact is expressed by saying that the perigee 
and of course the apogee, revolves, and that the line 
which joins these tw^o points, or the fine of the apsides, 
also revolves. 

171. The inequalities of the moon's motions are di- 
vided into periodical and secular. Periodical inequft 
ities are those which are completed in comparatively 
short periods. Secular inequalities are those which 
are completed only in very long periods, such as cen- 
turies or ages. Hence the corresponding terms peri- 
odical equations and secular equations. As an exam- 
ple of a secular inequality, we may mention the ac- 
celeration of the moon^s mean motion. It is discov- 
ered, that the moon actually revolves around the earth 



170. In what period does the line of the apsides revolve? 
Explain what is meant by this. 



136 THE MOON. 

in less time now than she did in ancient times. The 
difference however is exceedingly small, being only 
about 10" in a century, but increases from century to 
century as the square of the number of centuries. This 
remarkable fact was discovered by Dr. Halley.* In a 
lunar ecHpse the moon's longitude differs from that of 
the sun, at the middle of the eclipse, by exactly 180° ; 
and since the sun's longitude at any given time of the 
year is known, if we can learn the day and hour when 
an eclipse occurs, we shall of course know the longitude 
of the sun and moon. Now in the year 721 before the 
Christian era, on a specified day and hour, Ptolemy re- 
cords a lunar eclipse to have happened, and to have been 
observed by the Chaldeans. The moon's longitude, 
therefore, for that time is known ; and as we know the 
mean motions of the moon at present, starting from that 
epoch, and computing, as may easily be done, the place 
which the moon ought to occupy at present at any given 
time, she is found to be actually nearly a degree and a 
half in advance of that place. Moreover, the same con- 
clusion is derived from a comparison of the Chaldean 
observations with those made by an Arabian astronomer 
of the tenth century. 

This phenomenon at first led astronomers to appre- 
hend that the moon encountered a resisting medium, 
which, by destroying at every revolution a small portion 
of her projectile force, would have the eftect to bring 
9tr nearer and nearer to the earth and thus to augment 
her velocity. But in 1786, La Place demonstrated that 



171, How are the inequalities of the moon's motions divided? 
"What are periodical inequalities ? What are secular inequali- 
ties ? Give an example of a secular hiequality. How is it 
known that the moon's motions are accelerated ? What is the 
amount of the acceleration per century 1 Will they always 
continue to be accelerated ? 



* Astronomer Royal of Great Britain, and cotemporary with Sir Isaac 
Newton. 



ECLIPSES. 13y' 

this acceleration is one of the legitimate effects of the 
sun's disturbing force, and is so connected with changes 
in the eccentricity of the earth's orbit, that the moon 
will continue to be accelerated while that eccentricity 
diminishes, but w^hen the eccentricity has reached its 
minimum (as it will do after many ages) and begins to 
increase, then the moon's motion will begin to be re- 
tarded, and thus her motions will oscillate forever about 
a mean value. 



CHAPTER V. 



OF ECLIPSES. 



172. An Eclipse of the moon happens when the moon 
in its revolution around the earth, falls into the earth's 
shadow. An Eclipse of the sun happens when the 
moon coming between the earth and the sun, covers 
either a part or the whole of the solar disk. 

The earth and the moon being both opake globular 
bodies exposed to the sun's hght, they cast shadows op- 
posite to the sun like any other bodies on which the 
sun shines. Were the sun of the same size with the 
earth and the moon, then the lines drawn touching the 
surface of the sun, and the surface of the earth or momi 
(which lines form the boundaries of the shadow) woula 
be parallel to each other, and the shadow would be a 
cylinder infinite in length ; and were the sun less than 
the earth or the moon, the shadow would be an increas- 
ing cone, its narrower end resting on the earth ; but as 



172. When does an eclipse of the moon happen ? When 
does an eclipse of the sun happen ? Were the sun of the same 
size with the earth and moon, how would their shadows be ? 
How if less than these bodies 1 How are they in fact? Ex- 
plain bv figure 32 

12* 



138 



THE MOON. 



the sun is vastly greater than either of these bodies, 
the shadow of each is a cone, whose base rests on the 
body itself, and which comes to a point or vertex at a 
certain distance behind the body. These several cases 
are represented in the following diagrams. 

Fig. 32. 




173. It is found by calculation, that the length of the 
moon's shadow is, on an average, just about sufficient to 
reach to the earth, but the moon is sometimes farther 
from the earth than at others. (Art. 16G.) When she is 
nearer than usual, the shadow reaches considerably be- 
yond the surface of the earth. Also the moon as well 
as the earth, is at different distances from the sun at dif- 
ferent times, and its shadow is longest when it is far- 
thest from the sun. Now when both these circumstan- 
^s conspire, that is, when the moon is in her perigee 
and in her aphelion, her shadow extends nearly 15000 
miles beyond the center of the earth, and covers a space 



173. How does the moon's shadow compare with her dis- 
tance from the earth ? When does her shadow extend farthest 
beyond the center of the earth ' What is the greatest breadth 
of her shadow where it falls on the surface of the earth ? What 
is the length of the earth's shadow ? When only can an eclipse 
of the sun take place ? When only can an eclipse of the moon 
occur ? Explain from figure 33. What is the moon's Pen- 
umbra 1 



139 



on the surface of the earth 170 miles broad. The 
earth's shadow is towards a miUion of miles in length, 
and more than three and a half times as long as the dis- 
tance from the earth to the moon ; and it is also at the 
distance of the moon three times as broad as the moon 
itself. An eclipse of the sun can take place only at new 
moon, when the sun and moon meet in the same part of 
the heavens, for then only can the moon come between 
us and the sun ; and an eclipse of the moon can occur 
only w^hen the sun and moon are in opposite parts of 
the heavens, or at full moon, for then only can the moon 
fall into the shadow of the earth. 

The nature of eclipses will be clearly understood from 
the following representation. This figure • exhibits the 

Fig. 33. 




relative position of the sun, the earth, and the moon, 
both in a solar and in a lunar eclipse. It is evident from 
the figure, that if a spectator were situated v/here the 
moon's shadow strikes the earth, the moon would cut off 
from him the view of the sun, or the sun would be to- 
tally ecHpsed. Or, if he were within a certain distance 
of the shadow on either side, the moon would be partly 
between him and the sun, and would intercept from 
him more or less of the sun's light, according as he was 
nearer to the shadow or farther from it. If he were at 
c, or a, he would just see the moon entering upon the 



140 THE MOON. 

sun's disk ; if he were nearer the shadow than either of 
these points, he would have a portion of the sun's Hght 
cut off from his view, and the moment he entered the 
shadow itself, he w^ould lose sight of the sun. To all 
places between c or d and the shadow, the sun would 
cast a partial shadow of the moon, growing deeper and 
deeper as it approached the true shadow. This partial 
shadow is called the moon's Penumbra. In like man- 
ner, as the moon approaches the earth's shadow in a lu- 
nar eclipse, as soon as she arrives at «, the earth begins 
to intercept from her a portion of the sun's light, or she 
falls into the earth's penumbra. She continues to lose 
more and more of the sun's light as she draws near to 
the shadow, and hence her disk becomes gradually ob- 
scured, until it enters the shadow^, where the sun's light 
is entirely lost. 

174. As the sun and earth are both situated in the 
plane of the ecliptic, if the moon also revolved around 
the earth in this plane, we should have a solar eclipse at 
every new moon, and a lunar eclipse at every full 
moon ; for in the former case the moon would come di- 
rectly between us and the sun, and in the latter case, 
the earth would come directly between the sun and the 
moon. But the moon's path is inclined to the ecliptic 
about 5°, and the center of the moon may be all this 
distance from the center of the sun, at new moon, and 
the same distance from the center of the earth's shadow 
at full moon. It is true the moon extends across her 
path, one half her breadth lying on each side of it, and 
the sun likewise reaches from the ecliptic a distance 
equal to half his breadth. But these luminaries to- 
gether make but little more than a degree, and conse- 
quently their two semi-diameters would occupy only 



174. Why do we not have a solar eclipse every new moon, 
and a lunar eclipse every full moon ? Explain how eclipses 
occur only when the sun is near one of the moon's nodes, by 
fi<Ture 34. 



i 



ECLIPSES. 141 

about half a degree of the five degrees from one orbit 
to the other. Also the earth's shadow where the moon 
crosses it extends from the ecliptic less than three 
fourths of a degree, so that the semi-diameter of the 
moon and of the earth's shadow, would together reach 
but Httle way across the space that may in certain cases 
separate the two luminaries from each other when they 
are in opposition. Thus suppose we could take hold 
of the circle in the figure that represents the moon's 
orbit, (Fig. 31,) and lift the moon up five degrees above 
the plane of the paper, it is evident that the moon 
as seen from the earth, would appear in the heavens 
five degreess above the sun, and of course would cut off 
none of his light, and that the moon at the full would 
pass the shadow of the earth five degrees below it, and 
would suffer no eclipse. But in the course of the sun's 
apparent revolution around the earth once a year, he is 
successively in every part of the ecliptic ; consequently, 
the conjunctions and oppositions of the sun and moon 
may occur at any part of the ecliptic, and of course at 
the two points where the moon's orbit crosses the eclip- 
tic, that is, at the nodes, for the sun must necessarily 
come to each of these nodes once a year. If then the 
moon overtakes the sun just as she is crossing his path, 

Fig. 34. 




she will hide more or less of his disk from us. Since, 
also, the earth's shadow is always directly opposite to 
the sun, if the sun is at one of the nodes, the shadow 



142 THE MOON. 

must extend in the direction of the other node, so as to 
lie directly across the moon's path, and if the moon over- 
takes it there, she will pass through it and be eclipsed. 
Thus in figure 34, let BN represent the sun's path, and 
AN the moon's, N being the place of the node ; then it is 
evident that if the tvs^o luminaries at new moon be so 
far from the node, that the distance between their centers 
is greater than their semi-diameters, no eclipse can hap- 
pen ; but if that distance is less than this sum as at 
E, F, then an eclipse will take place, but if the position 
be as at C, D, the two bodies will just touch one another. 
If A denote the earth's shadow instead of the sun, the 
same illustration will apply to an eclipse of the moon. 

175. Since bodies are defined to be in conjunction 
when they are in the same part of the heavens, and to 
be in opposition when they are in opposite parts of the 
heavens, it may not appear how the sun and moon can 
be in conjunction as at A and B, when they are still at 
some distance from each other. But it must be recol- 
lected that bodies are in conjunction when they have the 
same longitude, in which case they are both situate^ in 
the same great circle perpendicular to the ecliptic, that 
is, in the same secondary to the ecliptic. One of the 
bodies may be much farther from the ecliptic than the 
other ; still, if the same secondary to the ecliptic passes 
through them both, they will be in conjunction or oppo- 
sition. 

176. In a total eclipse of the moon, its disk is still 
visible, shining with a dull red light. This light cannot 
be derived directly from the sun, since the view of the 
sun is completely hidden from the moon ; nor by reflex- 
ion from the earth, since the illuminated side of the 



175. Is it necessary for two bodies to be precisely together 
in order to be in conjunction ? 

176. Why is the disk of the moon still visible in a total 
eclipse of the moon ? 



' ECLIPSES. 143 

earth is wholly turned from the moon ; but it is owing 
to refraction from the earth's atmosphere, by which a 
few scattered rays of the sun are bent round into the 
earth's shadow and conveyed to the moon, sufficient in 
number to afford the feeble light in question. 

177. It is impossible fully to understand the method 
of calculating eclipses, without a knowledge of trigo- 
nometry ; still it is not difficult to form some general no- 
tion of the process. It may be readily conceived that, 
by long continued observations on the sun and moon, 
the exact places which they will occupy in the heavens 
at any future times, may be forseen and laid down in 
tables of the sun and moon's motions ; that we may thus 
ascertain by inspecting the tables the exact instant when 
these two bodies will appear together in the heavens, or 
be in conjunction, and when they will be 180" apart, 
or in opposition. Moreover, since the exact place of the 
moon's node among the stars at any particular time is 
known to astronomers, it cannot be difficult to determine 
when the new or full moon occurs in the same part of 
the heavens as that where the node is projected as seen 
from the earth. In short, as astronomers can easily de- 
termine what will be the relative position of the sun, 
the moon, and the moon's nodes for any given time, 
they can tell when these luminaries will meet so near 
the node as to produce an eclipse of the sun, or when 
they will be in opposition so near the node as to produce 
an eclipse of the moon. 

178. Let us endeavor to form a just conception of the 
manner in which these three bodies, the sun, the earth, 
and the moon, are situated with respect to each other at 
the time of a solar eclipse. First, suppose the conjunction 
to take place at the node. Then the straight line which 
connects the center of the sun and the earth, also passes 



177. What science must be known in order fully to under- 
stand the mode of calculating eclipses 1 Explain the general 
principles of the calculation. 



144 THE MOON. 

through the center of the moon, and coincides with the 
axis of its shadow ; and, since the earth is bisected by 
the plane of the ecHptic, the shadow would traverse the 
earth in the direction of the terrestrial ecliptic, from 
west to east, passing over the middle regions of the 
earth. Here the diurnal motion of the earth being in 
the same direction with the shadow, but with a less ve- 
locity, the shadow will appear to move with a speed 
equal only to the difference between the two. Secondly, 
suppose the moon is on the north side of the ecliptic at 
the time of conjunction, and moving towards her de- 
scending node, and that the conjunction takes place 
as far from the node as an eclipse can happen. The 
shadow will not fall in the plane of the ecliptic, but 
a little northward of it, so as just to graze the earth 
near the pole of the ecliptic. The nearer the conjunc- 
tion comes to the node, the farther the shadow will fall 
from the pole of the ecliptic towards the equatorial re- 
gions. 

179. The leading particulars respecting an eclipse 
OF THE SUN, are ascertained very nearly like those of a 
lunar eclipse. The shadow of the moon travels over a 
portion of the earth, as the shadow of a small cloud, seen 
from an eminence in a clear day, rides along over hills 
and plains. Let us imagine ourselves standing on the 
moon ; then we shall see the earth partially eclipsed by 
the shadow of the moon, in the same manner as we 
now see the moon eclipsed by the earth's shadow. 

But, although the general characters of a solar eclipse 
might be investigated on these principles, so far as re- 
spects the earth at large, yet as the appearances of the 
same eclipse of the sun are very different at different 
places on the earth's surface, it is necessary to calculate 



178. Explain the relative position of the sun, the earth, and 
the moon, in a solar eclipse. Explain the circumstances when 
the conjunction takes place at the node, and when it occurs at 
a distance from the node. 



ECLIPSES. 145 

its peculiar aspects for each place separately, a circum- 
stance which makes the calculation of a solar eclipse 
much more complicated and tedious than of an eclipse 
of the moon. The moon, Vv^hen she enters the shadow 
of the earth, is deprived of the light of the part immer- 
sed, and that part appears black alike to all places where 
the moon is above the horizon. But it is not so with a 
solar eclipse. We do not see this by the shadow cast 
on the earth, as w^e should do if we stood on the moon, 
but by the interposition of the moon betw-een us and the 
sun ; and the sun may be hidden from one observer 
while he is in full view of another only a few miles dis- 
tant. Thus, a small insulated cloud sailing in a cleai- 
sky, will, for a few moments, hide the sun from us, and 
from a certain space near us, while all the region around 
is illuminated," 

We have compared the motion of the moon's shadow 
over the surface of the earth to that of a cloud ; but its 
velocity is incomparably greater. The mean motion of 
the moon around the earth is about 33' per hour ; but 
33' of the moon's orbit is 2280 miles, and the shadow 
moves of course at the same rate, or 2280 miles per 
hour, traversing the entire disk of the earth in less than 
four hours. 

180. The diameter of the moon's shadow where it 
eclipses the earth can never exceed 170 miles, and com- 
monly falls much short of that ; and the greatest por- 
tion of the earth's surface ever covered by the moon's 
penumbra is about 4393 miles, 

181. The apparent diameter of the moon is sometimes 
larger than that of the sun, sometimes smaller, and 



179. How are the leading particulars of an eclipse of the sun 
ascertained ? How illustrated by the motion of a cloud ? In 
what respects does the calculation of a solar differ from that of 
a lunar eclipse ? How does the shadow of the moon compare 
with that of a cloud in velocity ? 



146 



THE MOON. 



sometimes exactly equal to it. Suppose an observer 
placed on the right line which joins the centers of the 
sun and moon ; if the apparent diameter of the moon is 
greater than that of the sun, the ecHpse will be total. If 
the two diameters are equal, the moon's shadow just 
reaches the earth, and the sun is hidden but for a mo- 
ment from the view of spectators situated in the line 
which the vertex of the shadow describes on the surface 
of the earth. But if, as happens when the moon comes 
to her conjunction in that part of her orbit which is to- 
wards her apogee, the moon's diameter is less than the 
sun's, then the observer will see a ring of the sun en- 
circling the moon, constituting an Annular Eclipse^ as in 
figure 35. 

Fig. 35. 




180. What cannot the diameter of the moon's shadow- 
where it eclipses the earth, exceed ? What is the greatest 
portion of the earth's surface ever covered by the moon's pe- 
numbra ? 

181. How does the moon's apparent diameter compare with 
the sun's ? When will the eclipse be total, and when annular ? 



ECLIPSES. 14T 

182. Eclipses of the sun are modified by the eleva- 
tion of the moon above the horizon, since its apparent 
diameter is augmented as its altitude is increased. This 
effect, combined with that of parallax, may so increase 
or diminish the apparent distance between the centers of 
the sun and moon, that from this cause alone, of two 
observers at a distance from each other, one might see 
an eclipse which was not visible to the other. If the 
horizontal diameter of the moon differs but little from 
the apparent diameter of the sun, the case might occur 
where the eclipse would be annular over the places 
where it was observed morning and evening, but total 
where it was observed at mid-day. 

The earth in its diurnal revolution and the moon's 
shadow both move from west to east, but the shadow 
moves faster than the earth ; hence the moon overtakes 
the sun on its western limb and crosses it from west to 
east. The excess of the apparent diameter of the moon 
above that of the sun in a total eclipse is so small, that 
total darkness seldom continues longer than four minutes, 
and can never continue so long as eight minuutes. An 
annular eclipse may last 12m. 24s. 

183. Eclipses of the sun are more frequent than those 
of the moon. Yet lunar eclipses being visible to every 
part of the terrestrial hemisphere opposite to the sun, 
while those of the sun are visible only to the small por- 
tion of the hemisphere on which the moon's shadow 
falls, it happens that for any particular place on the 
earth, lunar echpses are more frequently visible than 
solar. In any year, the number of eclipses of both lu- 



182. How are eclipses of the sun modified by the elevation 
of the moon above the horizon ? How might the same eclipse 
appear total to one observer and annular to another ? How 
long can total darkness continue in a solar echpse ? How long 
may an annular eclipse last ? 

183. Whichare most frequent, solar or lunar eclipses ? Why 
does an eclipse of the moon sometimes happen at the next full 
moon after an eclipse of the sun ? 



148 REVOLUTIONS. 

minaries cannot be less than two nor more than seven : 
the most usual number is four, and it is very rare to 
have more than six. A total eclipse of the moon fre- 
quently happens at the next full moon after an eclipse 
of the sun. For since, in an eclipse of the sun, the sun 
is at or near one of the moon's nodes, the earth's shadow 
must be at or near the other node, and may not have 
passed far from the node before the moon overtakes it. 

184. In total eclipses of the sun, there has sometimes 
been observed a remarkable radiation of light from the 
margin of the sun. This has been ascribed to an illu- 
mination of the solar atmosphere, but it is with more 
probability owing to the zodiacal light, which at that 
time is projected around the sun, and which is of such 
dimensions as to extend far beyond the solar orb.* 

A total eclipse of the sun is one of the most sublime 
and impressive phenomena of nature. Among barbarous 
tribes it is ever contemplated with fear and astonish- 
ment, while among cultivated nations it is recognized, 
from the exactness with which the time of occurrence 
and the various appearances answer to the prediction, as 
affording one of the proudest triumphs of astronomy. 
By astronomers themselves it is of course viewed with 
the highest interest, not only as verifying their calcula- 
tions, but as contributing to establish beyond all doubt 
the certainty of those grand laws, the truth of which is 
involved in the result. During the eclipse of June, 
1806, which was one of the most remarkable on record, 
the time of total darkness, as seen by the author of this 
work, was about mid-day. The sky was entirely cloud- 



1 84. How is the radiation of light around the margin of the 
sun in a total eclipse of the sun, accounted for ? How have 
eclipses of the sun been regarded among barbarous tribes ? 
How among civilized nations ? How by astronomers ? Give 
some account of the great eclipse of 1806. 

♦ See an excellent description and delineation of this appearance as 
it was exhibited in the eclipse of 1806, in the Transactions of the Al- 
bany Institute, by the late Chancellor De Witt. 



ECLIPSES. 149 

less, but as the period of total obscuration approached, a 
gloom pervaded all nature. When the sun was wholly- 
lost sight of, planets and stars came into view ; a fearful 
pall hung upon the sky, unlike both to night and to 
twilight ; and, the temperature of the air rapidly de- 
clining, a sudden chill came over the earth. Even the 
animal tribes exhibited tokens of fear and agitation. 

185. The word Eclipse is derived from a Greek word, 
{ey.leixiiig,) which signifies to fail, to faint, or swoon 
away, since the moon at the period of her greatest 
brightness falling into the shadow of the earth, was im- 
agined by the ancients to sicken and swoon, as if she 
were going to die. By some very ancient nations she 
was supposed at such times to be in pain, and hence 
lunar eclipses were called the labors of the moon, (lunae 
labores ;) and, in order to relieve her fancied distress, they 
lifted torches high in the atmosphere, blew horns and 
trumpets, beat upon brazen vessels, and even, after the 
eclipse was over, they offered sacrifices to the moon. 
The opinion also extensively prevailed, that it was in 
the power .of witches, by their spells and charms, not 
only to darken the moon, but to bring her down from 
her orbit, and to compel her to shed her baleful influences 
upon the earth. In a solar eclipse also, especially when 
total, the sun was supposed to turn away his face in ab- 
horrence of some atrocious crime, that either had been 
perpetrated or was about to be perpetrated, and to 
threaten mankind with everlasting night, and the de- 
struction of the world. 

The Chinese, who from a very high period of anti- 
quity have been great observers of eclipses, although 
they did not take much notice of those of the moon, re- 
garded echpses of the sun in general as unfortunate, but 
especially such as occurred on the first day of the year. 



185. From what is the word eclipse derived ? What ideas 
had certain ancient nations respecting eclipses 1 With what 
ceremonies did they observe them ? How were eclipses re- 
garded among the Chinese 1 

13* 



150 THE MOON. 

These were thought to forbode the greatest calamities 
to the emperor, who on such occasions did not receive 
the usual compliments of the season. When an eclipse 
of the sun was expected from the predictions of their as- 
tronomers, they made great preparation at court for ob- 
serving it ; and as soon as it commenced, a blind man 
beat a drum and a great concourse assembled, and the 
Mandarins, or nobility, appeared in state. 

186. From 1831 to 1838, was a period distinguished 
for great eclipses of the sun, in which time there were no 
less than five, of the most remarkable character. The 
next total eclipse of the sun, visible in the United States, 
will occur on the 7th of August, 1869. 



CHAPTER VI. 

OF LONGITUDE. TIDES. 

187. As eclipses of the sun afford one of the most 
approved methods of finding the longitude of ^^laces, our 
attention is naturally turned next towards that subject. 

The ancients studied astronomy in order that they 
might read their destinies in the stars : the moderns that 
they may securely navigate the ocean. A large portion 
of the refined labors of modern astronomy, has been di- 
rected towards perfecting the astronomical tables with 
the view of finding the longitude at sea, — an object 
manifestly worthy of the highest efforts of science, con- 
sidering the vast amount of property and of human life 
involved in navigation. 

188. The difference of longitude between two places, 
may he found by any method by which we can ascertain 



1S6. What recent period has abounded with gjeat eclipses 
of the sun ? When will the next total eclipse of the sun occur ? 

187. For what purpose did the ancients study astronomy ? 
For what purpose do the moderns study it ? 



LONGITUDE. 151 

the difference of their local times, at the same instant of 
absolute time. 

As the earth turns on its axis from west to east, any- 
place that lies eastward of another w^ill come sooner un- 
der the sun, or will have the sun earlier on the meridian, 
and consequently, in respect to the hour of the day, will 
be in advance of the other at the rate of one hour for 
every 15°, or four minutes of time for each degree. Thus, 
to a place 15° east of Greenwich, it is 1 o'clock, P. M. 
when it is noon at Greenwich; and to a place 15° west 
of that meridian, it is 11 o'clock, A. M. at the same in- 
stant. Hence the difference of time at any two places, 
indicates their difference of longitude. 

189. The easiest method of finding the longitude is 
by means of an accurate time piece, or chronometer. Let 
us set out from London with a chronometer accurately 
adjusted to Greenwich time, and travel eastward to a 
certain place, where the time is accurately kept, or may 
be ascertained by observation. We find, for example, 
that it is 1 o'clock by our chronometer, when it is 2 
o'clock and 30 minutes at the place of observation. 
Hence the longitude is 15 x 1.5=22J° E. Had we trav- 
elled westward until our chronometer was an hour and 
a half in advance of the time at the place of observa- 
tion, (that is, so much later in the day,) our longitude 
would have been 22|^o W. But it would not be neces- 
sary to repair to London in order to set our chronometer 
to Greenwich time. This might be done at any obser- 
vatory, or any place whose longitude has been accu- 



188. How may the difference of longitude between two pla- 
ces be found ? How many degrees of longitude correspond to 
one hour in time ? How many minutes to one degree ? 

189, Explain the method of finding the longitude by the 
chronometer. To what time is it set ? How do we ascertain 
the longitude of a place by it ? Would it be necessary to re- 
pair to Greenwich to regulate our chronometer ? What is said 
of the accuracy of some chronometers ? Why is not this 
method adapted to general use ? 



152 THE MOON. 

rately determined. For example, the time at New YorK 
is 4h. 56m. 4s.5 behind that of Greenwich. If, there- 
fore, we set our chronometer so much before the true 
time at New York, it will indicate the time at Green- 
wich. Moreover, on arriving at different places any 
where on the earth, whose longitude is accurately known, 
we may learn whether our chronometer keeps accurate 
time or not, and if not, the amount of its error. Chro- 
nometers have been constructed of such an astonishing 
degree of accuracy, as to deviate but a few seconds in a 
voyage from London to Baffin's Bay and back, during an 
absence of several years. But chronometers which are 
sufficiently accurate to be depended on for long voya- 
ges, are too expensive for general use, and the means of 
verifying their accuracy are not sufficiently easy. More- 
over, chronometers^ by being transported from one place 
to another, change their daily rate, or depart from that 
mean rate which they preserve at a fixed station. A 
chronometer, therefore, cannot be relied on for determin- 
ing the longitudes of places where the greatest degree of 
accuracy is required, especially where the instrument is 
conveyed over land, although the uncertainty attendant 
on one instrument may be nearly obviated by employing 
several and taking their mean results. 

190. Eclipses of the sun and moon are sometimes 
used for determining the longitude. The exact instant 
of immersion or of emersion, or any other definite mo- 
ment of the eclipse which presents itself to tw^o distant 
observers, affords the means of comparing their difference 
of time, and hence of determining their difference of 
longitude. Since the entrance of the moon into the 
earth's shadow, in a lunar eclipse, is seen at the same 
instant of absolute time at all places where the eclipse 
is visible, this observation would be a very suitable one 
for finding the longitude were it not that, on account of 



1 90. Explain how to find the longitude by eclipses of the sun 
and moon. What objections are there to this method, both in 
lunar and solar eclipses 1 



LONGITUDE. 153 

the increasing darkness of the penumbra near the boun- 
daries of the shadow, it is difficult to determine the pre- 
cise instant when the moon enters the shadow. By- 
taking observations on the immersions of known spots 
on the lunar disk, a mean result may be obtained which 
will give the longitude with tolerable accuracy. In an 
eclipse of the sun, the instants of immersion and emer- 
sion may be observed with greater accuracy, although, 
since these do not take place at the same instant of ab- 
solute time, the calculation of the longitude from obser- 
vations on a solar eclipse are complicated and laborious. 

191. The lunar method of finding the longitude, at 
sea, is in many respects preferable to every other. It 
consists in measuring (with a sextant) the angular dis- 
tance between the moon and the sun, or between the 
moon and a star, and then turning to the Nautical Alma- 
nac,* and finding what time it was at Greenwich when 
that distance was the same. The moon moves so rap- 
idly, that this distance will not be the same except at 
very nearly the same instant of absolute time. For ex- 
ample, at 9 o'clock, A. M., at a certain place, we find the 
angular distance of the moon and the sun to be 12^ ; 
and, on looking into the Nautical Almanac, we find that 
the time when this distance was the same for the me- 
ridian of Greenwich was 1 o'clock, P. M. ; hence w^e 
infer that the longitude of the place is four hours, or 60° 
west. 



191. Explain the lunar method of finding the longitude. 
What measurements are made 1 How do we find the corres- 
ponding time at Greenwich 1 



* The Naxdical Almanac, is a book published annually by the British 
Board of Longitude, containing various tables and astronomical infor- 
mation for the use of navigators. The American Almanac also con- 
tains a variety of astronomical information, peculiarly interesting to the 
people of tlie United States, in connexion with a vast amount of 
statistical matter. It is well deserving of a place in the library of the 
student. 



154 THE MOON. 

The Nautical Almanac contains the true angular dis- 
tance of the moon from the sun, fro/a the four large 
planets, (Venus, Mars, Jupiter, and Saturn.) and from 
nine bright fixed stars, for the beginning of every third 
hour of mean time for the meridian of Greenwich ; and 
the mean time corresponding to any intermediate hour, 
may be found by proportional parts.* 

192. It would be a very simple operation to determine 
the longitude by Lunar Distances, if the process as de- 
scribed in the preceding article were all that is neces- 
sary ; but the various circumstances of parallax, refrac- 
tion, and dip of the horizon, would differ more or less at 
the two places, even were the bodies, whose distances 
were taken, in view from both, which is not necessarily 
the case. The observations, therefore, require to be 
reduced to the center of the earth, being cleared of the 
effects of parallax and refraction. Hence, three obser- 
vers are necessary in order to take a lunar distance in 
the most exact manner, viz. two to measure the altitudes 
of the two bodies respectively, at the same time that 
the third takes the angular distance between them. 
The altitudes of the two luminaries at the time of ob- 
servation must be known, in order to estimate the effects 
of parallax and refraction. 

193. Although the lunar method of finding the longi- 
tude at sea has many advantages over the other meth- 
ods in use, yet it also has its disadvantages. One is, the 
great exactness requisite in observing the distance of 
the moon from the sun or star, as a small error in the 
distance makes a considerable error in the longitude. 
The moon moves at the rate of about a degree in two 



192. What difficulties are there in this method ? Why are 
three observers necessary ? 

193. What are the objections to this method ? What is the 
error of the best tables now in use ? 

» See Bowditch's Navigator, Tenth Ed. p. 226. 



LONGITUDE. 155 

hours, or one minute of space in two minutes of time. 
Therefore, if we make an error of one minute in ob- 
serving the distance, w^e make an error of two minutes 
in time, or 30 miles of longitude at the equator. A sin- 
gle observation with the best sextant, may be liable to 
an error of more than half a minute ; but the accuracy 
of the result may be much increased by a mean of sev- 
eral observations taken to the east and west of the moon. 
The imperfection of the lunar tables was until recently 
considered as an objection to this method. Until within a 
few years, the best lunar tables were frequently errone- 
ous to the amount of one minute, occasioning an error 
of 30 miles. The error of the best tables now in use 
will rarely exceed 7 or 8 seconds. 



194. The tides are an alternate rising and falling of 
the waters of the ocean, at regular intervals. They have 
a maximum and a minimum twice a day, twice a month, 
and twice a year. ^ Of the daily tide, the maximum is 
called High tide, and the minimum Low tide. The 
maximum for the month is called Spring tide, and the 
minimum Neap tide. The rising of the tide is called 
Flood and its falling Ehh tide. 

Similar tides, whether high or low, occur on opposite 
sides of the earth at once. Thus at the same time that it 
is high tide at any given place, it is also high tide on the 
inferior meridian, and the same is true of the low tides. 

The interval between two successive high tides is 
12h. 25m.; or, if the same tide be considered as return- 
ing to the meridian, after having gone around the globe, 



194. What are the tides ? When have they a maximum and 
a minimum ? Define the terms High and Low, Spring and 
Neap, Flood and Ebb tides. What two tides occur at the same 
time 1 What is the interval between two successive high tides ? 
How much later is the tide of to-day than the same tide of 
yesterday 1 What is the average height of the tide for the 
whole globe 1 To what extreme height does it sometimes rise 1 
Have mland lakes and seas any tides ? 



156 THE MOON. 

its return is about 50 minutes later than it occurred on 
the preceding day. In this respect, as well as in various 
others, it corresponds very nearly to the motions of the 
moon. 

The average height for the whole globe is about 2 J 
feet ; or, if the earth were covered uniformly with a 
stratum of water, the difference between the two diam- 
eters of the oval would be 5 feet, or more exactly 5 feet 
and 8 inches ; but its actual height at various places is 
very various, sometimes rising to 60 or 70 feet, and 
sometimes being scarcely perceptible.' At the same 
place also, the phenomena of the tides are very different 
at different times. 

Inland lakes and seas, even those of the largest class, 
as Lake Superior, or the Caspian, have no perceptible 
tide. 

195. Tides are caused by the unequal attraction of 
the sun and moon upon different parts of the earth. 

Suppose the projectile force by which the earth is car- 
ried forward in her orbit, to be suspended, and the earth 
to fall towards one of these bodies, the moon, for exam- 
ple, in consequence of their mutual attraction. Then,. 
if all parts of the earth fell equally towards the moon, 
no derangement of its different parts would result, any 
more than of the particles of a drop of water in its de- 
scent to the ground. But if one part fell faster than an- 
other, the different portions would evidently be separa- 
ted from each other. Now this is precisely what takes 
place with respect to the earth in its fall towards the 
moon. The portions of the earth in the hemisphere 
next to the moon, on account of being nearer to the 
center of attraction, fall faster than those in the oppo- 
site hemisphere, and consequently leave them behind. 
The solid earth, on account of its cohesion, cannot obey 



195. State the cause of the tides. What would be the con- 
sequence were the earth abandoned to the force exerted by 
the moon alone ? 



TIDES. 157 

this impulse, since all its different portions constitute 
one mass, which is acted on in the same manner as 
though it were all collected in the center ; but the wa- 
ters on the surface, moving freely under this impulse, 
endeavor to desert the solid mass and fall towards the 
moon. For a similar reason the waters in the opposite 
hemisphere falling less towards the moon than the solid 
earth are left behind, or appear to rise from the center 
of the earth. 

196. Let DEFG (Fig. 36,) represent the globe ; and, 
for the sake of illustrating the principle, we will sup- 
pose the waters entirely to cover the globe at a uniform 
depth. Let defg represent the solid globe, and the cir- 




cular ring exterior to it, the covering of waters. Let C 
be the center of gravity of the solid mass, A that of the 
hemisphere next to the moon, (for the center of gravity 
of a ring is within the ring,) and B that of the remoter 
hemisphere. Now the force of attraction exerted by 
the moon, acts in the same manner as though the solid 
mass were all concentrated in C, and the waters of each 
hemisphere at A and B respectively ; and (the moon be- 



1 96. Explain the tides upon the doctrine of the center of 
gravity. Where would the tide-wave always be seen were it 
not for impediments ? What are these 7 
14 



158 THE MOON. 

ing supposed above E) it is evident that A will tend to 
leave C, and C to leave B behind. The same must evi- 
dently be true of the respective portions of matter, of 
which these points are the centers of gravity. The wa- 
ters of the globe will thus be reduced to an oval shape, 
being elongated in the direction of that meridian which 
is under the moon, and flattened in the intermediate 
parts, and most of all at points ninety degrees distant 
from that meridian. 

Were it not, therefore, for impediments which prevent 
the force from producing its full effects, we might expect 
to see the great tide-wave, as the elevated crest is called, 
always directly beneath the moon, attending it regularly 
around the globe. But the inertia of the waters pre- 
vents their instantly obeying the moon's attraction, and 
the friction of the waters on the bottom of the ocean, 
still farther retards its progress. It is not therefore until 
several hours (differing at different places) after the 
moon has passed the meridian of a place, that it is high 
tide at that place. 

197. The sun has a similar action to the moon, but 
only one third as great. On account of the great mass 
of the sun compared with that of the moon, we might 
suppose that his action in raising the tides would be 
greater than that of the moon ; but the nearness of the 
moon to the earth more than compensates for the sun's 
greater quantity of matter. Let us, however, form a just 
conception of the advantage which the moon derives 
from her proximity. It is not that her actual amount of 
attraction is tlius rendered greater than that of the sun ; 
but it is that her attraction for the different parts of the 
earth is very unequal, while that of the sun is nearly 
uniform. It is the inequality of this action, and not the 
absolute force, that produces the tides. The diameter of 
the earth is ^^ of the distance of the moon, while it is 
less than TTrnTrrr of the distance of the sun. 



197. Explain the action of the sun in raising the tide ? Why 
is its effect less than that of the moon ? 



TIDES. 159 

198. Having now learned the general cause of the 
tides, we will next attend to the explanation of particu- 
lar phenomena. 

The Spring tides, or those which rise to an unusual 
height twice a month, are produced by the sun and 
moon's acting together ; and the Neap tides, or those 
which are unusually low twice a month, are produced 
by the sun and moon's acting in opposition to each 
other. The Spring tides occur at the syzigies : the 
Neap tides at the quadratures. At the time of new moon, 
the sun and moon both being on the same side of the 
earth, and acting upon it in the same Hne, their actions 
conspire, and the sun may be considered as adding so 
much to the force of the moon. We have already ex- 
plained how the moon contributes to raise a tide on the 
opposite side of the earth. But the sun as well as the 
moon raises its own tide-wave, which, at new moon, 
coincides with the lunar tide-wave. At full moon, also, 
the two luminaries conspire in the same way to raise 
the tide ; for we must recollect that each body contri- 
butes to raise the tide on the opposite side of the earth 
as well as on the side nearest to it. At both the con- 
junctions and oppositions, therefore, that is, at the syzi- 
gies, we have unusually high tides. But here also the 
maximum effect is not at the moment of the syzigies, 
but 36 hours afterwards. 

At the quadratures, the solar wave is lowest where the 
lunar wave is highest ; hence the low tide produced by 
the sun is subtracted from high water and produces the 
Neap tides. Moreover, at the quadratures the solar 
wave is highest where the lunar wave is lowest, and 
hence is to be added to the height of low water at the 
time of Neap tides. Therefore the difference between 
high and low water is only about half as great at Neap 
tide as at Spring tide. 



198. What is the cause of the Spring tides 1 Also of the 
Neap tides ? How long after the syzigies does the highest 
tide occur ? 



160 THE MOON. 

199. The variations of distance in the sun are not 
great enough to influence the tides very materially, but 
the variations in the moon's distance have a striking 
eflfect. The tides which happen when the moon is in 
perigee, are considerably greater than when she is in 
apogee ; and if she happens to be in perigee at the time 
of the syzigies, the Spring tide is unusually high. 
When this happens at the equinoxes, the highest tides 
of the year are produced. 

200. The declinations of the sun and moon have a 
considerable influence on the height of the tide. When 
the moon, for example, has no declination, or is in the 

Fig. 37. 



equator, as in figure 37,* the two tides will be exactly 
equal on opposite sides of the meridian in the same 
parallel. Thus a place in the parallel TT' will have 



199. How do the variations in the moon's distance from the 
earth affect the tides ? How are the tides when the moon is in 
perigee ? How when she in apogee ? When are the highest 
tides of the year produced ? 



* Diagrams like these are apt to mislead the learner, by exhibiting the 
protuberance occasioned by the tides as much greater than the reahty. 
We must recollect that it amounts, at the highest, to only a very few 
feet in eight thousand miles. Were the diagram, therefore, drawn in 
just proportions, the alteration of figure produced by the tides would 
be wholly insensible. 



TIDES. 161 

the height of one tide T2 and the other tide T'3. 
The tides are in this case greatest at the equator, and 
diminish gradually to the poles, where it will be low 
water during the whole day. When the moon is 
on the north side of the equator, as in figure 38, at 
her greatest northern declination, a place describing 
the parallel TT' will have T'3 for the height of the 

Fig. 38. 






tide when the moon is on the superior meridian, and T2 
for the height at the same time on the inferior me- 
ridian. Therefore, all places north of the equator will 
have the highest tide when the moon is above the hor- 
izon, and the lowest when she is below it ; the differ- 
ence of the tides diminishing towards the equator, where 
they are equal. In like manner, (the moon being still 
at M, Fig. 38, that is, having northern declination,) 
places south of the equator have the highest tides when 
the moon is below the horizon, and the lowest when she 
is above it. The circumstances are all reversed when 
the moon is south of the equator. 

201. The motion of the tide- wave, it should be re- 
marked, is not Si progressive motion, but a mere undula- 
tion, and is to be carefully distinguished from the cur- 



200. Explain the effect of the declinations of the sun and 
moon upon the tides. How will the upper and lower tides cor- 
respond when the moon is in the equator ? How when the 
moon is north of the equator ? Explain by figures 37, 38. 
14* 



162 THE MOON. 

rents to which it gives rise. If the ocean completely 
covered the earth, the sun and moon being in the equa- 
tor, the tide-vs^ave would travel at the same rate as the 
earth on its axis. Indeed, the correct way of conceiv- 
ing of the tide-wave, is to consider the moon at rest, 
and the earth in its rotation from west to east, as bringing 
successive portions of water under the moon, which 
portions being elevated successively at the same rate as 
the earth revolves on its axis, have a relative motion 
westward in the same degree. 

202. The tides of rivers, narrow bays, and shores 
far from the main body of the ocean, are not produced 
in those places by the direct action of the sun and moon, 
but are subordinate waves propagated from the great 
tide-wave. 

Lines drawn through all the adjacent parts of any 
tract of water, which have high water at the same time, 
are called cotidal lines. We may, for instance, draw a 
line through all places in the Atlantic Ocean which 
have high tide in a given day at 1 o'clock, and another 
through all places which have high tide at 2 o'clock. 
The cotidal line for any hour may be considered as rep- 
resenting the summit or ridge of the tide-wave at that 
time ; and could the spectator, detached from the earth, 
perceive the summit of the wave, he would see it travel- 
ing round the earth in the open ocean once in twenty- 
four hours, followed by another twelve hours distant, 
and both sending branches into rivers, bays, and other 
openings into the main land. These latter are called 
Derivative tides, while those raised directly by the ac- 
tion of the sun and moon, are called Primitive tides. 



201. Is the motion of the tide-wave progressive? if the 
ocean completely covered the earth and the sun and moon were 
in the equator, hovv would the tide-wave travel ? What is the 
most correct way of conceiving of the tide-wave ? 

202. How are the tides of rivers, &lc. produced? Define 
cotidal lines. What does the cotidal line for any hour repre- 
sent ? Distinguish between Primitive and Derivative tides. 



TIDES. 163 

203. The velocity with which the wave moves, will 
depend on various circumstances, but principally on the 
depth, and probably on the regularity of the channel. 
If the depth be nearly uniform, the cotidal hnes will be 
nearly straight and parallel. But if some parts of the 
channel are deep while others are shallow, the tide will 
be detained by the greater friction of the shallow places, 
and the cotidal lines will be irregular. The direction 
also of the derivative tide, may be totally different from 
that of the primative. Thus, (Fig. 39,) if the great 

Fig. 39. 




tide-wave, moving from east to west, be represented by 
the lines 1, 2, 3, 4, the derivative tide which is propa- 
gated up a river or bay, will be represented by the co- 
tidal lines 3, 4, 5, 6, 7. Advancing faster in the channel 
than next the bank, the tides will lag behind towards 
the shores, and the cotidal lines will take the form of 
curves as represented in the diagram. 



203. On what will the velocity of the tide- wave depend ? 
What circumstances will retard it ? Explain figure 39. 



164 THE MOON. 

204. On account of the retarding influence of shoals, 
and an uneven, indented coast, the tide-wave travels 
more slowly along the shores of an island than in the 
neighbouring sea, assuming convex figures at a little dis- 
tance from the island and on opposite sides of it. These 
convex lines sometimes meet and become blended in 
such a manner as to create singular anomalies in a sea 
much broken by islands, as well as on coasts indented 
with numerous bays and rivers. Peculiar phenomena 
are also produced, when the tide flows in at opposite 
extremities of a reef or island, as into the two opposite 
ends of Long Island Sound. In certain cases a tide- 
wave is forced into a narrow arm of the sea, and pro- 
duces very remarkable tides. The tides of the Bay of 
Fundy (the highest in the world) sometimes rise to 
the height of 60 or 70 feet ; and the tides of the rivei 
Severn, near Bristol in England, rise to the height of 40 
feet. 

205. The Unit of Altitude of any place, is the height 
of the maximum tide after the syzigies, being usually 
about 36 hours after the new or full moon. But as the 
amount of this tide would be affected by the distance of 
the sun and moon from the earth, and by their declina- 
tions, these distances are taken at their mean value, and 
the luminaries are supposed to be in the equator ; the 
observations being so reduced as to conform to these cir- 
cumstances. The unit of altitude can be ascertained 
by observation only. The actual rise of the tide de- 
pends much on the strength and direction of the wind. 
When high winds conspire with a high flood tide, as is 
frequently the case near the equinoxes, the tide often 



204. How does the tide-wave travel along the shores of an 
island ? How are the great tides of the Bay of Fundy accounted 
for? How high do they rise there, and at Bristol in England ? 

205. Define the unit of altitude. By what circumstances is 
the unit of altitude affected 1 How is it ascertained ? State 
it for several places. 



TIDES. 165 

rises to a very unusual height. We subjoin from the 
American Almanac a few examples of the unit of alti- 
tude for different places. 

Feet. 
Cumberland, head of the Bay of Fundy, 71 
Boston, Hi 

New Haven, 8 

New York, 5 

Charleston, S. C, 6 

206. The Establishment of any port is the mean in- 
terval between noon and the time of high water, on the 
day of new or full moon. As the interval for any given 
place is ahvays nearly the same, it becomes a criterion 
of the retardation of the tides at that place. On ac- 
count of the importance to navigation of a correct 
knowledge of the tides, the British Board of Admiralty, 
at the suggestion of the Royal Society, recently issued 
orders to their agents in various important naval s-tations, 
to have accurate observations made on the tides, with 
the view of ascertaining the establishment and various 
other particulars respecting each station ; and the gov- 
ernment of the United States is prosecuting similar in- 
vestigations respecting our own ports. 

207. According to Professor Whewell, the tides on 
the coast of North America are derived from the great 
tide-wave of the South Atlantic, which runs steadily 
northward along the coast to the mouth of the Bay of 
Fundy, where it meets the northern tide-wave flowing 
in the opposite direction. Hence he accounts for the 
high tides of the Bay of Fundy. 

208. The largest lakes and inland seas have no per- 
ceptible tides. This is asserted by all writers respect- 



206. What is the establishment of a port ? What efforts 
have been made to obtain accurate observations on the tides ? 



166 THE MOON. 

ing the Caspian and Euxine, and the same is found to 
be true of the largest of the North American lakes, 
Lake Superior. 

Although these several tracts of water appear large 
when taken by themselves, yet they occupy but small 
portions of the surface of the globe, as will appear ev- 
ident from the delineation of them on an artificial globe. 
Now we must recollect that the primitive tides are pro- 
duced by the unequal action of the sun and moon upon 
the different parts of the earth ; and that it is only at 
points whose distance from each other bears a consider- 
able ratio to the whole distance of the sun or the moon, 
that the inequality of action becomes manifest. The 
space required is larger than either of these tracts of 
water. It is obvious also that they have no opportunity 
to be subject to a derivative tide. 

209. To apply the theory of universal gravitation to 
all the varying circumstances that influence the tides, 
becomes a matter of such intricacy, that La Place pro- 
nounces " the problem of the tides" the most difficult 
problem of celestial mechanics. 

210. The Atmosphere that envelops the earth, must 
evidently be subject to the action of the same forces as 
the covering of waters, and hence we might expect a 
rise and fall of the barometer, indicating an atmospheric 
tide corresponding to the tide of the ocean. La Place 
has calculated the amount of this aerial tide. It is too 
inconsiderable to be detected by changes in the barom- 
eter, unless by the most refined observations. Hence it 
is concluded, that the fluctuations produced by this cause 
are too slight to affect meteorological phenomena in any 
appreciable degree. 



207. How are the tides on the coast of North America de- 
rived ? 

208. Why have lakes and seas no tides ? 

209. What is said of the difficulty of applying the principle 
of universal gravitation to all the circumstances of the tides ? 



167 



CHAPTER VII. 

OP THE PLANETS THE INFERIOR PLANETS, MERCURY 

AND VENUS. 

211. The name planet signifies a wanderer* and is 
applied to this class of bodies because they shift their 
positions in the heavens, whereas the fixed stars con- 
stantly maintain the same places with respect to each 
other. The planets known from a high antiquity, are 
Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To 
these, in 1781, w^as added Uranus,f (or iiZersc/ie/, as it is 
sometimes called from the name of its discoverer,) and, 
as late as the commencement of the present century, 
four more were added, namely, Ceres, Pallas, Juno, and 
Vesta. These bodies are designated by the following 
characters : 



1. Mercury 


^ 


7. Ceres 


? 


2. Venus 


5 


8. Pallas 


$ 


3. Earth 


e 


9. Jupiter 


U 


4. Mars 


^ 


10. Saturn 


^ 


5. Vesta 


s 


11. Uranus 


^ 


6. Juno 


§ 







The foregoing are called the primary planets. Sev- 
eral of these have one or more attendants, or satellites, 



210. Has the atmosphere any tide 1 Is it sufficient to influ- 
ence meteorological phenomena ? 

211. Whence is the name planet derived ? Which of the 
planets have been long known ? Which have been added in 
modern times 1 Mark on paper or on the black board, the 
several characters by which the planets are designated. Dis- 
tinguish between the primary and the secondary planets. What 
bodies have satellites ? State the whole number of planets. 

♦ From tiie Greek TT\avriTT]s. t From Ovpavos. 



168 THE PLANETS. 

which revolve around them, as they revolve around the 
sun. The earth has one satellite, namely, the moon ; 
Jupiter has four ; Saturn, seven ; and Uranus, six. These 
bodies also are planets, but in distinction from the others 
they are called secondary planets. Hence, the w^hole 
number of planets are 29, viz. 11 primary, and 18 sec- 
ondary planets. 

212. With the exception of the four new planets, 
these bodies have their orbits very nearly in the same 
plane, and are never seen far from the ecliptic. Mer- 
cury, whose orbit is most inclined of all, never departs 
farther from the ecHptic than about 7°, while most of 
the other planets pursue very nearly the same path with 
the earth, in their annual revolutions around the sun. 
The new planets, however, make wider excursions from 
the plane of the ecliptic, amounting, in the case of Pal- 
las, to 34i°. 

213. Mercury and Venus are called inferior planets, 
because they have their orbits nearer to the sun than 
that of the earth ; while all the others, being more dis- 
tant from the sun than the earth, are called superior 
planets. The planets present great diversity among 
themselves in respect to distance from the sun, magni- 
tude, time of revolution, and density. They differ also 
in regard to satellites, of which, as we have seen, three 
have respectively four, six, and seven, while more than 
half have none at all. It will aid the memory, and 
render our view of the planetary system more clear and 
comprehensive, if we classify, as far as possible, the 
various particulars comprehended under the foregoing 
heads. 



212. Near what great circle are the orbits of all the planets ? 
How far doe.s Pallas deviate from the ecHptic ? 

213. Why are Mercury and Venus called Inferior planets T 
Why are the other planets called superior ? What diversities 
do the planets exhibit among themselves ? 



DISTANCES FROM THE SUN. 



169 



214. DISTANCES FROM THE SUN. 



1. Mercury, 

2. Venus, 
S. Earth, 

4. Mars, 

5. Vesta, 

6. Juno, 

7. Ceres, 

8. Pallas, 

9. Jupiter, 

10. Saturn, 

11. Uranus, 



37,000,000 

68,000,000 

95,000,000 

142,000,000 

225,000,000 

V 261,000,000 

485,000,000 

890,000,000 

1800,000,000 



The dimensions of the planetary system are seen 
from this table to be vast, comprehending a circular 
space thirty six hundred millions of miles in diameter. 
A railway car, travelling constantly at the rate of 20 
miles an hour, would require more than 20,000 years to 
cross the orbit of Uranus. 

It may aid the memory to remark, that in regard to 
the planets nearest the sun, the distances increase in an 
arithmetical ratio, while those most remote, increase in 
a geometrical ratio. Thus, if we add 30 to the distance 
of Mercury, it gives us nearly that of Venus ; 30 more 
gives that of the Earth ; while Saturn is nearly twice 
the distance of Jupiter, and Uranus twice the distance 
of Saturn. Between the orbits of Mars and Jupiter, a 
great chasm appeared, which broke the continuity of the 
series ; but the discovery of the new planets has filled 
the void. 



214. State the distance of each of the planets from the sun. 
What is said of the dimensions of the planetary system ? How 
do the distances of those planets which are nearest the sun in- 
crease 1 Also those which are more distant ? How may the 
mean distances of the planets from the sun be determined ? 
Give an example in computing the distance of Jupiter. 
15 



170 THE PLANETS. 

The mean distances of the planets from the sun, may- 
be determined by means of Kepler's law, that the squares 
of the periodical times are as the cubes of the distances. 
Thus the earth's distance being previously ascertained 
by means of the sun's horizontal parallax, and the pe- 
riod of any other planet, as Jupiter, being lea rned from 
observation, we say as 365.2562 : 4332.5852* : : 1^ : 
5.202^ which equals the cube of Jupiter's distance from 
the sun, and its root equals that distance itself. 

215. MAGNITUDES. 

Diam. in Miles. Mean apparent Diam. Volume. 

Mercury, 

Venus, 

Earth, , 

Mars, 
. Ceres, 
i- Jupiter, . 

Saturn, . 
> Uranus, . 

We remark here a great diversity in regard to magni- 
tude, a diversity which does not appear to be subject to 
any definite law. While Venus, an inferior planet, is 
y®o as large as the earth. Mars, a superior planet is only ^, 
while Jupiter is 1281 times as large. Although several 
of the planets, when nearest to us, appear brilliant and 
large when compared with the fixed stars, yet the angle 
which they subtend is very small, that of Venus, the 
greatest of all, never exceeding about T, or more exactly 
61 ".9, and that of Jupiter being when greatest only 
about f of a minute. 



3140 


6".9 


tV 


7700 


61".9 


t^ 


7912 




1 


4200 


6'^.3 


\ 


160 


0".5 




89000 


36^7 


1281 


. 79000 


16".2 


995 


35000 


4".0 


80 



215. State the diameter of each of the planets. What diver- 
sities occur in regard to their magnitudes ? How great angles 
do Venus and Jupiter subtend ? 

* This is the number of days in one revolution of Jupiter. 



PERIODIC TIMES MERCURY AND VENUS. 171 

216. PERIODIC TIMES. 





Revolution in its orbit. 




Mean daily motion. 


Mercury, 


3 months, 


or 


88 


days, 


4° 5^ 32".6 


Venus, 


7i " 


a 


224 




1° 36' 7^8 


Earth, 


1 year, 


" 


365 




0° 59' 8^3 


Mars, 


2 years. 


a 


687 




0° 31' 26".7 


Ceres, 


4 " 


it 


1681 




0° 12' 50".9 


Jupiter, 


12 " 


ti 


4332 




0° 4' 59".3 


Saturn, 


29 " 


a 


10759 


« 


0° 2' 0^^.6 


Uranus, 


84 " 


a 


30686 


« 


0° 0' 42" A 



From this view, it appears that the planets nearest the 
sun move most rapidly. Thus Mercury performs nearly 
350 revolutions while Uranus performs one. This is 
evidently not owing merely to the greater dimensions of 
the orbit of Uranus, for the length of its orbit is not 50 
times that of the orbit of Mercury, while the time em- 
ployed in describing it is 350 times that of Mercury. 
Indeed this ought to follow from Kepler's law that the 
squares of the periodical times are as the cubes of the 
distances, from which it is manifest that the times of 
revolution increase faster than the dimensions of the or- 
bit. Accordingly, the apparent progress of the most 
distant planets is exceedingly slow, the daily rate of 
Uranus being only 42^',4 per day ; so that for weeks and 
months, and even years, this planet but slightly changes 
its place among the stars. 

THE INFERIOR PLANETS, MERCURY AND VENUS. 

217. The inferior planets. Mercury and Venus, hav- 
ing their orbits so far within that of the earth, appear to 
us as attendants upon the sun. Mercury never appears 
farther from the sun than 29° (28° 48^ and seldom so 



216. State the periojiic time of each of the planets. Which 
planets move most rapidly 1 How many revolutions does Mer- 
cury perform while "Uranus performs one ? What is the daily 
rate of Uranus ? 



172 



THE PLANETS. 



far; and Venus never more than about" 47° (47^ 12'). 
Both planets, therefore, appear either in the west soon 
after sunset, or in the east a little before sunrise. In 
high latitudes, where the twilight is prolonged, Mercury 
can seldom be seen with the naked eye, and then only 
at the periods of its greatest elongation.* The reason 
of this will readily appear from the following diagram. 

Fig. 40. 




Let S (Fig. 40,) represent the sun, ADB the orbit of 
Mercury, and E the place of. the Earth. Each of the 
planets is seen at its greatest elongation, when a line, 
EA or EB in the figure, is a tangent to its orbit. Then 
the sun being at S' in the heavens, the planet will be 



217. What is Mercury's greatest elongation from the sun ? 
What is Venus's ? What is said respecting the difficulty of see- 
ing Mercury ? Explain by figure 40. 



• Copernicus is said to liave lamented on his death-bed that he had 
never been able to obtain a sight of Mercury, and Delambre saw it but 
twice. 



MERCURY AND VENUS. 173 

seen at A' and B^, when at its greatest elongations, and 
will appear no further from the sun than the arc S'A' or 
S'B' respectively. 

218. A planet is said to be in Conjunction with the 
sun, when it is seen in the same part of the heavens 
with the sun, or when it has the same longitude. Mer- 
cury and Venus have each two conjunctions, the inferior, 
and the superior. The inferior conjunction is its posi- 
tion when in conjunction on the same side of the sun 
with the earth, as at C in the figure : the superior con- 
junction is its position when on the side of the sun most 
distant from the earth, as at D. 

219. The period occupied by a planet between two 
successive conjunctions with the earth, is called its sy- 
nodical revolution. Both the planet and the earth being 
in motion, the time of the synodical revolution exceeds 
that of the sidereal revolution of Mercury or Venus ; 
for when the planet comes round to the place where it 
before overtook the earth, it does not find the earth at 
that point, but far in advance of it. Thus, let Mercury 
come into inferior conjunction with the earth at C, (Fig. 
40.) In about 88 days, the planet will come round to 
the same point again ; but meanwhile the earth has 
moved forward through the arc EE', and will continue 
to move while the planet is moving more rapidly to over^ 
take her, the case being analogous to that of the hour 
and minute hand of a clo^k. 

The synodical period of Mercury is 116, and of Venus 
584 days. 



218. When is a planet said to be in conjunction with the 
sun ? What conjunctions have the inferior planets \ 

219. Define the synodical revoluticUr How does this period 
compare with the sidereal revolution ? Explain by figure 40. 
What is the synodical period of Mercury and Venus respecl- 
ively ? 

15* 



174 THE PLANETS. 

220, The motion of an inferior planet is direct in 
passing through its superior conjunction, and retrogade 
in passing through its inferior conjunction. Thus Ve- 
nus, while going from B through D to A, (Fig. 40,) 
moves in the order of the signs, or from west to east, 
and would appear to traverse the celestial vault B'S'A' 
from right to left ; hui in passing from A through C to 
B, her course would be retrogade, returning on the same 
arc from left to right. If the earth were at rest, there- 
fore, (and the sun, of course, at rest,) the inferior planets 
would appear to oscillate backwards and forwards across 
the sun. But, it must be recollected, that the earth is 
moving in the same direction with the planet, as respects 
the signs, but with a slow^er motion. This modifies the 
motions of the planet, accelerating it in the superior and 
retarding it in the inferior conjunctions. Thus in figure 
40, Venus while moving through BDA would seem to 
move in the heavens from B' to A' w^ere the earth at 
rest ; but meanw^hile the earth changes its position from 
E to E' by w'hich means the planet is not seen at A' 
but at A", being accelerated by the arc A' A" in conse- 
quence of the earth's motion. On the other hand, when 
the planet is passing through its inferior conjunction 
ACB, it appears to move backwards in the heavens from 
A' to B' if the earth is at rest, but from A' to B" if the 
earth has in the mean time moved from E to E' being 
retarded by the arc B'B". Although the motions of the 
earth have the effect to accelerate the planet in the superi- 
or conjunction, and to retard it^in the inferior, yet, on ac- 
count of the greater distance, the apparent motion of the 
planet is much slower in the superior than in the infe- 
rior conjunction. 

221. When passing from the superior to the inferior 
conjunction, or from the inferior to the superior conjunc- 



220. When is the motion of an interior planet direct and 
when retrograde ? Explain by figure 40, If the earth were at 
rest, how would the inferior planets appear to move ? Show 
how the earth's motion modifies the apparent motions. 



MERCURY AND VENUS. 175 

tion, through the greatest elongations, the inferior plan- 
ets are stationary. 

If the earth were at rest, the stationary points would 
be at the greatest elongations as at A and B, for then the 
planet would be moving directly towards or from the 
earth, and would be seen for some time in the same 
place in the heavens ; but the earth itself is moving 
nearly at right angles to the line of the planet's motion, 
that is, the Hne which is drawn from the earth to the 
planet through the point of greatest elongation ; hence a 
direct motion is given to the planet by this cause. When 
the planet, however, has passed this line by its superior 
velocity, it soon overcomes this tendency of the earth to 
give it a relative motion eastward, and becomes retro- 
grade as it approaches the inferior conjunction. Its sta- 
tionary point obviously lies between its place of greatest 
elongation, and the place where its motion becomes re- 
trograde. Mercury is stationary at an elongation of 
from 15° to 20° from the sun ; and Venus at about 29°. 

222. Mercury and Venus exhibit to the telescope, pha- 
ses similar to those of the moon. 

When on the side of their inferior conjunction, these 
planets appear horned, like the moon in her first and last 
quarters ; and when on the side of their superior con- 
junctions they appear gibbous. At the moment of su- 
perior conjunction, the whole enlightened orb of the 
planet is turned towards the earth, and the appearance 
would be that of the fuU moon, but the planet is too 
near the sun to be commonly visible. 

These different phases show these bodies are opake, 
and shine only as they reflect to us the light of the sun ; 
and the same remark applies to all the planets. 



221. When are the inferior planets stationary? Why are 
they not stationary at the points of greatest elongation ? At what 
elongation are Mercury and Venus stationary respectively ? 

222. What phases do Mercury and Venus exhibit ? Explain 
by figure 40, W^hence do these bodies derive their light ? Is 
the same true of the other planets 1 



176 THE PLANETS. 

223. The orbit of Mercury is the most eccentric, and 
the most inclined of all the planets ;* while that of Ve- 
nus varies hut little from a circle, and lies much nearer 
to the ecliptic. 

The eccentricity of the orbit of Mercury is nearly J- 
its semi-major axis, while that of Venus is only. ■j\-s ; 
the inclination of Mercury's orbit is 7°, while that of 
Venus is less than 3J°. Mercury, on account of his dif- 
ferent distances from the earth, varies much in his appa- 
rent diameter, which is only 5" in the apogee, but 12" 
in the perigee. The inclination of his orbit to his equa- 
tor being very great, the changes of his seasons must be 
proportionally great. 

These different aspects of an inferior planet will be 
easily understood from Fig. 41, where the earth is at E^ 
Fig. 41. 




B 

and the planet is represented in various positions in its 
revolutions around the sun. When at A, in the supe- 
rior conjunction, the whole enlightened disk is turned 
towards us ; at D, in the inferior conjunction, the en- 
lightened side is turned entirely from us ; and at the 
quadratures B and C, half the disk is in view. Between 
A and B, and A and C, the planet is gibbous, like the 
moon in her second and third quarters ; and between B 



223. What is said of the eccentricity and inclination of the 
orbit of Mercury ? How does the apparent diameter of Mer- 
cury vary 1 How are his changes of seasons ? 

* The new planets of course excepted. 



MERCURY AND VENUS. 177 

and D, and C and D, the planet is horned, like the moon 
in her first and last quarters. 

224. An inferior planet is brightest at a certain point 
between its greatest elongation and inferior conjunction. 

Its maximum brilliancy would happen at the inferior 
conjunction, (being then nearest to us,) if it shined by 
its own light ; but in that position its dark side is turned 
towards us. Still, its maximum cannot be when most 
of the illuminated side is towards us ; for then, being at 
the superior conjunction, it is at its greatest distance 
from us. The maximum must therefore be somewhere 
between the two. Venus gives her greatest light when 
about 40° from the sun. 

225. Mercury and Venus oth revolve on their axes, 
in nearly the same time with the earth. 

The diurnal period of Mercury is 24h. 5m. 28s., and 
that of Venus 23h. 21m. 7s. The revolutions on their 
axes have been determined by means of some spot or 
mark seen by the telescope, as the revolution of the sun 
on his axis is ascertained by means of his spots. 

226. Venus is regarded as the most beautiful of the 
planets, and is well known as the morning and evening 
star. The most ancient nations did not indeed recog- 
nize the evening and morning star as one and the same 
body, but supposed they were different planets, and ac- 
cordingly gave them different names, calling the morn- 
ing star Lucifer, and the evening star Hesperus. At her 
period of greatest splendor, Venus casts a shadow, and is 
sometimes visible in broad daylight. Her Hght is then 
estimated as equal to that of twenty stars of the first 



224. When is an inferior planet brightest ? Why not when 
nearest to us ? Why not when most of the illuminated side is 
turned towards us ? 

225. In what time do Mercury and Venus, respectively, re- 
volve on their axes ? How are these periods ascertained ? 



178 THE PLANETS. 

magnitude. At her period of greatest elongation, Ve- 
nus is visible from three to four hours after the setting 
or before the rising of the sun. 

227. Every eight years, Venus forms her conjunctions 
with the sun in the same "part of the heavens. 

For, since the synod ical period of Venus is 584 days, 
and her sidereal period 224.7, 

224.7 : 360° : : 584 : 935.6== the arc of longitude de- 
scribed by Venus between the first and second conjunc- 
tions. Deducting 720°, or two entire circumferences, 
the remainder, 215°.6, shows how far the place of the 
second conjunction is in advance of the first. Hence, 
in five synodical revolutions, or 2920 days, the same 
point must have advanced 215°. 6 x 5 = 1078°, which is 
nearly three entire circumferences, so that at the end of 
five synodical revolutions, occupying 2920 days, or 8 
years, the conjunction of Venus takes place nearly in 
the same place in the heavens as at first. 

Whatever appearances of this planet, therefore, arise 
from its position w^ith respect to the earth and the sun, 
they are repeated every eight years in nearly the same 
form. 

TRANSITS OF THE INFERIOR PLANETS. 

228. The Transit of Mercury or Venus, is its passage 
across the sun^s disk, as the moon passes over it in a solar 
eclipse. 

As a transit takes place only when the planet is in 
inferior conjunction, at which time her motion is retro- 
grade, it is always from left to right, and the planet is 
seen projected on the solar disk in a black round spot. 



226. What erroneous notions had the ancients respecting the 
morning and evening star ? What is said of the brilliancy of 
Venus at her greatest splendor ? How long may Venus be in 
sight after sunset ? 

227. What happens to Venus every eight years ? 



MERCURY AND VENUS. 179 

Were the orbits of the inferior planets coincident with 
the plane of the earth's orbit, a transit would occur to 
some part of the earth at every inferior conjunction. 
But the orbit of Venus makes an angle of 3^"^ with the 
ecliptic, and Mercury an angle of 7^ ; and, moreover, 
the apparent diameter of each of these bodies is very 
small, both of which circumstances conspire to render a 
transit a comparatively rare occurrence, since it can hap- 
pen only when the sun, at the time of an inferior con- 
junction, chances to be at or extremely near the planet's 
node. The nodes of Mercury lie in longitude 46° and 
226°, points which the sun passes through in May and 
IVovember. It is only in these months, therefore, that 
transits of Mercury can occur. For a similar reason, 
those of Venus occur only in June and December. Since, 
however, the nodes of both planets have a small retro- 
grade motion, the months in which transits occur will 
change in the course of ages 

22Q. Transits of Mercury occur more frequently than 
those of Venus. The periodic times of Mercury and 
the earth are so adjusted to each other, that Mercury 
performs nearly 29 revolutions while the earth performs 
7. If, therefore, the two bodies meet at the node in any 
given year, seven years afterwards they will meet nearly 
at the same node, and a transit may take place, accord- 
ingly, at intervals of 7 years. But 54 revolutions of 
Mercury correspond still nearer to 13 revolutions of the 



228. What is meant by the transit of Mercury or Venus ? 
When only can a transit take place 1 What angles do the or- 
bits of Venus and Mercury respectively make with the ecliptic 1 
In what months does the sun pa'ss through the nodes of each 
of these planets ? 

229. Which planet has the most frequent transits ? What is 
the shortest inter v^al of the transits of Mercury ? What are the 
longer intervals ? When will the next occur ? What are in- 
tervals of the transits of Venus ? When was the last transit 
of Venus, and when will the next occur ? 



180 THE PLANETS. 

earth, and therefore a transit is still more probable after 
intervals of 13 years. At intervals of 33 years, transits 
of Mercury are exceedingly probable, because in that 
time Mercuiy makes almost exactly 137 revolutions. 
Intermediate transits however may occur at the other 
node, these intervals having reference merely to the 
same node. Thus transits of Mercury happened at the 
ascending node in 1815, and 1822, at intervals of 
7 years ; and at the descending node in 1832, which 
will return in 1845, after an interval of 13 years. Tran- 
sits of Venus are much more unfrequent than those of 
Mercury. Eight revolutions of the earth are completed 
in nearly the same time as thirteen revolutions of Venus, 
and hence two transits of Venus may occur at an in- 
terval of 8 years, as was the case at the last return of 
this phenomenon, one transit having occurred in 1761, 
and another in 1769. But if a transit does not happen 
after 8 years, it will not happen, at the same node, until 
an interval of 235 years ; but intermediate transits may 
occur at the other node. The next transit of Venus will 
take place in 1874, being 235 years after the first that was 
ever observed, which occurred in the year 1639. In the 
mean time, as already mentioned, two transits have oc- 
curred at the other node, at intervals of 8 years. 

230. The great interest attached by astronomers to a 
transit of Venus, arises from its furnishing the most accu- 
rate means in our power of determining the sun^s hori- 
zontal parallax — an element of great importance, since it 
leads us to a knowledge of the distance of the earth from 
the sun, and, consequently, by the application of Kepler's 
law, (Art. 130,) of the distances of all the other planets. 
Hence, in 1769, great efforts were made throughout the 
civilized world, under the patronage of different govern- 



230. Why is so much interest attached to the transits of 
Venus ? What efforts were made to observe it in 1769 ? Why 
cannot we ascertain the horizontal parallax of the sun in the 
same way as we do that of the moon ? 



MERCURY AND VENUS. 181 

ments, to observe this phenomenon under circumstances 
the most favorable for determining the parallax of the 
sun. 

The common methods of finding the parallax of a 
heavenly body cannot be relied on to a greater degree 
of accuracy than 4". In the case of the moon, whose 
greatest parallax amounts to about 1°, this deviation 
from absolute accuracy is not material ; but it amounts 
to nearly half the entire parallax of the sun. 

231. If the sun and Yenus were equally distant from 
us, they would be equally affected by parallax as view^ed 
by spectators in different parts of the earth, and hence 
their relative situation w^ould not be altered by it ; but 
since Venus, at the inferior conjunction, is only about 
one third as far off as the sun, her parallax is propor- 
tionally greater, and therefore spectators at distant points 
will see Venus projected on different parts of the so- 
lar disk, as the planet traverses the disk. Astron- 
omers avail themselves of this circumstance to ascer- 
tain the sun's horizontal parallax. In order to make 
the difference as large as possible very distant pla- 
ces are selected for observation. Thus in the transit 
of 1769, among the places selected, tw^o of the most 
favorable were Wardhuz in Lapland, and Oteheite, one 
of the South Sea Islands. 

The appearance of Venus on the sun's disk, being 
that of a w^ell defined black spot, and the exactness with 
w^hich the moment of external or internal contact may 
be determined, are circumstances favorable to the exact- 
ness of the result ; and astronomers repose so much con- 
fidence in the estimation of the sun's horizontal parallax 
as derived from the observations on the transit of 1769, 
that this important element is thought to be ascertained 



231. How is Verms projected on the sun to spectators in 
diflerent parts of the earth 1 What places were selected for 
observing the transit of 1769 ? 
16 



182 THE PLANETS. 

within ^ of a second. The general result of all these 
observations gives the sun's horizontal parallax 8".6, or 
more exactly, 8/'5776. 

232. During the transits of Venus over the sun's disk 
in 1761 and 1769, a sort of penumbral light was ob- 
served around the planet by several astronomers, which 
was thought to indicate an atmosphere. This appear- 
ance was particularly observable while ihe planet was 
coming on and going off the solar disk. The total im- 
mersion and emersion were not instantaneous ; but as 
two drops of water when about to separate, form a liga- 
ment between them, so there was a dark shade stretched 
out between Venus and the sun, and when the ligament 
broke, the planet seemed to have got about an eighth part 
of her diameter from the limb of the sun. The various 
accounts of the two transits abound with remarks hke 
these, which indicate the existence of an atmosphere 
about Venus of nearly the density and extent of the 
earth's atmosphere. Similar proofs of the existence of 
an atmosphere around this planet, are derived from ap- 
pearances of twilight. 

The elder astronomers imagined they had discovered 
a satellite accompanying Venus in her transit. If Venus 
had in reality any satellite, the fact would be obvious at 
her transits, as the satellite would be projected near the 
primary on the sun's disk ; but later astronomers have 
searched in vain for any appearances of the kind, and 
the inference is that former astronomers were deceived 
by some optical illusion. 

Astronomers have detected very high mountains on 
Venus, sometimes reaching to the elevation of 22 miles ; 
and it is remarkable that the highest mountains in Ve- 
nus, in Mercury, in the moon, and in the earth, are al- 
ways in the southern hemisphere. 



232. What indications have been observed of an atmos- 
phere about Venus ? Has Venus any Satellite ? What is said 
of the mountains of Venus ? 



SUPERIOR PLANETS. 183 



CHAPTER VIII. 

OP THE SUPERIOR PLANETS MARS, JUPITER, SATURN, AND 

URANUS CERES, PALLAS, JUNO, AND VESTA. 

233. The Superior planets are distinguished from the 
Inferior, by being seen at all distances from the sun 
from 0° to 180^. Having their orbits exterior to that 
of t^e earth, they of course never come between us and 
the sun, that is, they never have any inferior conjunction 
like Mercury and Venus, but they are sometimes seen in 
superior conjunction, and sometimes in opposition. Nor 
do they, like the inferior planets, exhibit to the telescope 
different phases, but, with a single exception, they al- 
ways present the side that is turned towards the earth 
fully enlightened. This is owing to their great distance 
from the earth ; for were the spectator to stand upon the 
sun, he would of course always have the illuminated 
side of each of the planets turned towards him ; but, 
so distant are all the superior planets except Mars, that 
they are viewed by us very nearly in the same manner 
as they would be if we actually stood on the sun. 

234. Mars is a small planet, his diameter being only 
about half of that of the earth, or 4200 miles. He also, 
at times, comes nearer to the earth than any other planet 
except Venus. His mean distance from the sun is 
142,000,000 miles ; but bis orbit is so eccentric that his 
distance varies much in different parts of his revolution. 
Mars is alw^ays very near the ecliptic, never varying from 



233. Name the Superior Planets. How are they distin- 
guished from the Inferior 1 Which of them exhibits phases ? 
Why do not the rest ? 

234. Mars. — State his diameter — Mean distance from the 
sun — inclination of his orbit. How distinguished from the 
other planets ? Why do his brightness and apparent magni- 
tude vary so much ? Illustrate by figure 42. 



184 THE PLANETS. 

it 2°. He is distinguished from all the planets by his 
deep red color, and fiery aspect ; but his brightness and 
apparent magnitude vary much at different times, being 
sometimes nearer to us than at others, by the whole di- 
ameter of the earth's orbit, that is, by about 190,000,000 
of miles. When Mars is on the same side of the sun 
with the earth, or at his opposition, he comes within 
47,000,000 miles of the earth, and rising about the time 
the sun sets, surprises us by his magnitude and splen- 
dor ; but when he passes to the other side of the su« to 
his superior conjunction, he dwindles to the appearance 
of a small star, being then 237,000,000 miles from us. 
Thus, let M (Fig. 42,) represent Mars in opposition, 
and M^ in the superior conjunction, while E represents 
the earth. It is obvious that in the former situation, the 
planet must be nearer to the earth than in the latter 
by the whole diameter of the earth's orbit. 

Fig. 42. 




235. Mars is the only one of the superior planets 
which exhibits phases. When he is towards the quad- 
ratures at Q or Q', it is evident from the figure that 
only a part of the circle of illumination is turned towards 



MARS. 185 

the earth, such a portion of the remoter part of it being 
concealed from our view as to render the form more or 
less gibbous. 

236. When viewed with a powerful telescope, the 
surface of Mars appears diversified with numerous vari- 
eties of light and shade. The region around the poles 
is marked by white spots, which vary their appearance 
with the changes of seasons in the planets. Hence Dr. 
Herschel conjectured that they were owing to ice and 
snow, which alternately accumulates and melts, accord- 
ing to the position of each pole with respect to the sun. 
It has been common to ascribe the ruddy light of this 
planet to an extensive and dense atmosphere, which was 
said to be distinctly indicated, by the gradual diminution 
of light observed in a star as it approached very near to 
the planet in undergoing an occultation ; but more re- 
cent observations afford no such evidence of an atmos- 
phere. 

237. By observations on the spots, we learn that Mars 
revolves on his axis in very nearly the same time with 
the earth, (24h. 39m. 21s.3) ; and that the inclination of 
his axis to that of his orbit is also nearly the same, 
being 30° 18' lO^'.S. 

As the diurnal rotation of Mars is nearly the same as 
that of the earth, we might expect a similar flattening at 
the poles, giving to the planet a spheroidal figure. In- 
deed the compression or ellipticity of Mars greatly ex- 
ceeds that of the earth, being no less than \ of the 
equatorial diameter, while that of the earth is only 3-^^. 



235. Show why Mars should exhibit phases. 

236. How is the surface of Mars diversified ? What is seen 
around the poles ? What indications are there of ice and 
snow ? To what is the ruddy hue of Mars ascribed ? 

237. How do we learn his revolution on his axis 1 In what 
time does it take place 1 What is the figiure of Mars ? How 
does its ellipticity compare with that of the earth ? 

16* 



186 



THE PLANETS. 



This remarkable flattening of the poles of Mars has been 
supposed to arise from a great variation of density in the 
planet in different parts. 

238. Jupiter is distinguished from all the other plan- 
ets by his vast magnitude. His diameter is 89,000 
miles, and his volume 1280 times that of the earth. 
His figure is strikingly spheroidal, the equatorial being 
larger than the polar diameter in the proportion of 107 
to 100. Such a figure might naturally be expected 
from the rapidity of his diurnal rotation, which is ac- 
complished in about 10 hours. A place on^the equa- 
tor of Jupiter must turn 27 times as fast as on the ter- 
restrial equator. The distance of Jupiter from the sun 
is nearly 490,000,000 miles, and his revolution around 
the sun occupies nearly 12 years. 

239. The view^ of Jupiter through a good telescope, 
(Fig. 43,) is one of the most magnificent and interesting 
spectacles in astronomy. The disk expands into a large 

Fig. 43. 







and bright orb like the full moon ; the spheroidal fio-ure 
which theory assigns to revolving spheres, is here pal- 



238. Jupiter. — State his diameter, volume, fi^^^ure, revolu- 
tion on his axis, velocity of his equator, distance from the sun, 
periodic time. 



/ 



187 



pably exhibited to the eye ; across the disk, arranged 
in parallel stripes, are discerned several dusky bands, 
called belts ; and four bright satellites, always in at- 
tendance, and ever varying their positions, compose a 
splendid retinue. Indeed, astronomers gaze with pecu- 
liar interest on Jupiter and his moons, as affording a 
miniature representation of the whole solar system, 
repeating on a smaller scale, the same revolutions, and 
exemplifying, in a manner more within the compass 
of our observation, the same laws as regulate the 
entire assemblage of sun and planets. 

240. The Belts of Jupiter are variable in their num- 
ber and dimensions. With the smaller telescopes, only 
one or two are seen across the equatorial regions ; but 
with more powerful instruments, the number is in- 
creased, covering a great part of the whole disk. Dif- 
ferent opinions have been entertained by astronomers 
respecting the cause of the belts ; but they have gen- 
erally been regarded as clouds formed in the atmo- 
sphere of the planet, agitated by winds, as is indicated 
by their frequent changes, and made to assume the 
form of belts parallel to the equator by currents that 
circulate around the planet like the trade winds and 
other currents that circulate around our globe. Sir 
John Herschel supposes that the belts are not ranges 
of clouds, but portions of the planet itself brought into 
view by the removal of clouds and mists, that exist in 
the atmosphere of the planet through which are open- 
ings made by currents circulating around Jupiter. 

241. The Satellites of Jupiter may be seen with a 
telescope of very moderate powers. Even a common 
spy glass will enable us to discern them. Indeed one or 
two of them have been occasionally seen with the naked 
eye. In the largest telescopes, they severally appear as 



239. What does the telescopic view of Jupiter exhibit? 
Why do astronomers regard it with so much interest ? 

240. Describe Jupiter's Belts — to what are they ascribed? 



188 



THE PLANETS. 



bright as Sirius. With such an instrument, the view of 
Jupiter with his moons and belts is truly a magnificent 
spectacle, a world within itself. As the orbits of the 
satellites do not deviate far from the plane of the eclip- 
tic, and but little from the equator of the planet, they 
are usually seen in nearly a straight line with each other 
extending across the central part of the disk. 

242. Jupiter's satellites are distinguished from one 
another by the denominations o^ first, second, third, and 
fourth, according to their relative distances from Jupiter, 
the first being that which is nearest to him. Their ap- 
parent motion is oscillatory, like that of a pendulum, 
going alternately from their greatest elongation on one 
side to their greatest elongation on the other, sometime-s 
in a straight line, and sometimes in an elliptical curve, 
according to the different points of view in which we 
observe them from the earth. They are sometimes sta- 
tionary ; their motion is alternately direct and retro- 
grade ; and, in short, they exhibit in miniature all the 
phenomena of the planetary system. Various partic- 
ulars of the system are exhibited in the following table. 
The distances are given in radii of the primary. 



Satellite. 


Diameter. 


Mean Distance. 


Sidereal Revolution. 


1 


2508 


6.04853 


Id. 18h. 28m. 


2 


2068 


9.62347 


3 13 14 


3 


3377 


15.35024 


7 3 43 


4 


2890 


26.99835 


16 16 32 



Hence it appears, first, that Jupiter's satellites are all 
except the second, somewhat larger than the moon, but 
that the second satellite is the smallest, and the third 
the largest of the whole, but the diameter of the latter 
is only about 2V P^^t of that of the primary ; secondly, 
that the distance of the innermost satelhte from the planet 



241. How do the satellites appear to the telescope ? 

242. Describe the motions of the satellites — magnitudes — 
distances — periods of revolution. 



JUPITER. 189 

is three times his diameter, while that of the outermost 
satellite is nearly fourteen times his diameter ; thirdly, 
that the first satellite completes his revolution around the 
primary in one day and three fourths, while the fourth 
satellite requires nearly sixteen and three fourths days. 

243. The orbits of the satellites are nearly or quite 
circular, and deviate but little from the plane of the 
planet's equator, and of course are but slightly inclined 
to the plane of its orbit. They are, therefore, in a sim- 
ilar situation with respect to Jupiter as the moon would 
be with respect to the earth if her orbit nearly coincided 
with the ecliptic, in which case she would undergo an 
eclipse at every opposition. 

244. The ecHpses of Jupiter's satellites, in their gen- 
eral conception, are perfectly analogous to those of the 
moon, but in their detail they differ in several particulars. 
Owing to the much greater distance of Jupiter from the 
sun, and its greater magnitude, the cone of its shadow is 
much longer and larger than that of the earth. On this 
account, as well as on account of the little inclination of 
their orbits to that of their primary, the three inner sat- 
ellites of Jupiter pass through the shadow, and are totally 
eclipsed at every revolution. The fourth satellite, ow- 
ing to the greater inclination of its orbit, sometimes 
though rarely escapes eclipse, and sometimes merely 
grazes the limits of the shadow or suffers a partial 
eclipse. These eclipses, moreover, are not seen, as is 
the case with those of the moon, from the center of 
their motion, but from a remote station, and one whose 
situation with respect to the line of the shadow is vari- 
able. This, of course, makes no difference in the times 
of the eclipses, but a very great one in their visibility, 



243. What is the shape of their orbits 1 How situated with 
regard to the plane of the planet's orbit ? 

244. Describe the phenomena of their eclipses. Which of 
them escapes an eclipse 1 Are these eclipses seen in different 
parts of the earth at the same moment of absolute time 1 



190 THE PLANETS. 

and in their apparent situations with respect to the 
planet at the moment of their entering or quitting the 
shadow. 

245. The edipses of Jupiter's satellites present some 
curious phenomena, which will be understood from the 
following diagrams. 

Fig. 44. 





Let A, B, C, D, (Fig. 44,) represent the earth in dif- 
ferent parts of its orbit ; J, Jupiter in his orbit sur- 
rounded by his four satelHtes the orbits of which are 
marked 1, 2, 3, 4. At a the first satellite enters the 
shadow of the planet, and emerges from it at &, and ad- 
vances to its greatest elongation at c. The other satellites 
traverse the shadow in a similar manner. These ap- 
pearances will be modified by the place the earth hap- 
pens to occupy in its orbit, being greatly altered by per- 
spective ; but their appearances for any given night as 
exhibited at Greenwich, are calculated and accurately 
laid down in the Nautical Almanac. 

When one of the satellites is passing between Jupiter 
and the sun it casts its shadow on the primary as the 



245. Describe the phenomena of the eclipses from figure 44. 
"Will these appearances be affected by the relative position of 
the earth, with respect to the planet ? Does the shadow of a 
satellite or the satellite itself ever make a transit across the 
disk of the planet ? 



r 



JUPITER. 191 

moon casts its shadow on the earth in a solar eclipse. 
We see with the telescope, the shadow traversing the 
disk. Sometimes the satellite itself is seen projected on 
the disk ; but being illuminated as well as the primary, 
it is not so easily distinguished as Venus or Mercury, 
when seen on the sun's disk, since, at the time of their 
transits, their dark sides are turned towards us. The 
manner in which these phenomena take place, as seen 
from the earth in the several positions, A, B, C, D, may 
be conceived by attentively inspecting the figure. It 
will be seen, that when the earth is at A or C, the im- 
mersions and emersions must take place close to the disk 
of the planet, but that, in other positions of the earth, as 
at B or D, the satellite will be seen to enter and leave 
the shadow at some distance from the primary. 

246. The eclipses of Jupiter's satelHtes have been 
studied with great attention by astronomers, on account 
of their affording one of the easiest methods of deter- 
mining the longitude. On this subject Sir J. Herschel 
remarks : The discovery of Jupiter's satellites by Gali- 
leo, which was one of the first fruits of the invention of 
the telescope, forms one of the most memorable epochs 
in the history of astronomy. The first astronomical so- 
lution of the great problem of " the longitude," — the 
most important problem for the interests of mankind 
that has ever been brought under the dominion of strict 
scientific principles, dates immediately from their dis- 
covery. The final and conclusive establishment of the 
Copernican system of astronomy, may also be considered 
as referable to the discovery and study of this exquisite 
miniature system, in which the laws of the planetary 
motions, as ascertained by Kepler, and especially that 
which connects their periods and distances, were speed- 
ily traced, and found to be satisfactorily maintained. 



246. Why have the eclipses of Jupiter's satellites been stud- 
ied with so much attention 1 Who first discovered these eclip- 
ses 1 What bearing has the system of Jupiter and his satel- 
lites upon the Copernican system of astronomy ? 



192 THE PLANETS. 

247. The entrance of one of Jupiter's satellites into 
the shadow of the primary being seen like the entrance 
of the moon into the earth's shadow, at the same mo- 
ment of absolute time, at all places where the planet is 
visible, and being wholly independent of parallax ; be- 
ing, moreover, predicted beforehand with great accuracy 
for the instant of its occurrence at Greenwich, and given 
in the Nautical Almanac ; this would seem to be one of 
those events (Art. 188.) which are peculiarly adapted for 
finding the longitude. It must be remarked, however, 
that the extinction of light in the satellite at its immer- 
sion, and the recovery of its light at its emersion, are not 
instantaneous but gradual ; for the satellite, like the 
moon, occupies some time in entering into the shadow 
or in emerging from it, which occasions a progressive 
dimunition or increase of light. The better the light 
afforded by the telescope with which the observation is 
made, the later the satellite will be seen at its immer- 
sion, and the sooner at its emersion.* In noting the 
eclipses even of the first satellite, the time must be con- 
sidered as uncertain to the amount of 20 or 30 seconds ; 
and those of the other satellites involve still greater un- 
certainty. Two observers, in the same room, observing 
with different telescopes the same echpse, will frequently 
disagree in noting its time to the amount of 15 or 20 
seconds ; and the difference will be always the same 
way. 

Better methods, therefore, of finding the longitude are 
now employed, although the facility with which the 
necessary observations can be made, and the little calcu- 
lation required, still render this method eligible in many 



247. Explain how these eclipses are used in finding the lon- 
gitude. What imperfections attend this method ? Is this meth- 
od much employed at present ? Why can it not be used at 



* This is the reason why observers are directed in tlie Nautical Al- 
manac to use telescopes of a certain power. 



SATURN. 193 

cases where extreme accuracy is not important. As a 
telescope is essential for observing an eclipse of one of 
the satellites, it is obvious that this method cannot be 
practiced at sea, 

248. The grand discovery of the progressive motion 
of light, was first made by observations on the eclipses 
of Jupiter's satelhtes. In the year 1 675, it was remarked 
by Roemer, a Danish astronomer, on comparing together 
observations of these eclipses during many successive 
years, that they take place sooner by about sixteen min- 
utes, (16m.26s.6) when the earth is on the same side of 
the sun with the planet, than when she is on the oppo- 
site side. This difference he ascribed to the progressive 
motion of light, which takes that time to pass through the 
diameter of the earth's orbit, making the velocity of light 
about 192,000 miles per second. So great a velocity star- 
tled astronomers at first, and produced some degi'ee of 
distrust of this explanation of the phenomenon ; but the 
subsequent discovery of what is called the aberration of 
light, led to an independent estimation of the velocity of 
light with almost precisely the same result. 

249. Saturn comes next in the series as w^e recede 
from the sun, and has, like Jupiter, a system within it- 
self, on a scale of great magnificence. In size it is, next 
to Jupiter, the largest of the planets, being 79,000 miles 
in diameter, or about 1,000 times as large as the earth. 
It has likewise belts on its surface and is attended by 
seven satellites. But a still more wonderful appendage 
is its Ring, a broad wheel encompassing the planet at a 
great distance from it. We have already intimated that 
8aturn's system is on a grand scale. As, however, Sat- 



248. How was the progressive motion of light first discovered? 
Explain the manner of the discovery. How long is light in 
traversing the diameter of the earth's orbit ? What is its ve- 
locity per second 1 How does this agree with that derived 
from the aberration of light ? 

17 



194 



THE PLANETS. 



urn is distant from us nearly 900,000,000 miles, we are 
unable to obtain the same clear and striking views of 
his phenomena as we do of the phenomena of Jupiter, al- 
though they really present a more wonderful mechanism. 

250. Saturn's ring, when viewed with telescopes of 
a high power, is found to consist of two concentric rings, 
separated from each other by a dark space. Although 
this division of the rings appears to us, on account of 
our immense distance, as only a fine Hne, yet it is in re- 
ality an interval of not less than about 1800 miles. The 
dimensions of the whole system are in round numbers 
as follows : 

Miles. 

Diameter of the planet, .... 79,000 
From the surface of the planet to the inner ring, 20,000 

Breadth of the inner ring, .... 17,000 

Interval between the rings, .... 1,800 

Breadth of the outer ring, .... 10,500 

Extreme dimensions from outside to outside, 176,000 
Fig. 45. 




The figure represents Saturn as it appears to a power- 
ful telescope, surrounded by its rings, and having its body 
striped with dark belts, somewhat similar but broader 



249. Saturn. — State his diameter and volume, number of 
satellites, ring, distance from the sun. 



SATURN. 195 

and less strongly marked than those of Jupiter, and 
owing doubtless to a similar cause. That the ring is a 
solid opake substance, is shown by its throwing its shad- 
ow on the body of the planet on the side nearest the sun 
and on the other side receiving that of the body. From 
the parallelism of the belts with the plane of the ring, 
it may be conjectured that the axis of rotation of the 
planet is perpendicular to that plane ; and this conjec- 
ture is confirmed by the occasional appearance of exten- 
sive dusky spots on its surface, which when watched 
indicate a rotation parallel to the ring in lOh. 29m. 17s. 
This motion, it will be remarked, is nearly the same 
wdth the diurnal motion of Jupiter, subjecting places on 
the equator of the planet to a very swift revolution, and 
occasioning a high degree of compression at the poles, 
the equatorial being to the polar diameter in the high 
ratio of 11 to 10. It requires a telescope of high mag- 
nifying powers and a strong light, to give a full and 
striking view of Saturn with his rings and belts and sat- 
tellites ; for we must bear in mind, that in the distance 
of Saturn one second of angular measurement corres- 
ponds to 4,000 miles, a space equal to the semi-diameter 
of our globe. But with a telescope of moderate powers, 
the leading phenomena of the ring itself may be ob- 
served. 

251. Saturn's ring, in its revolution around the sun, 
always remains parallel to itself. 

If we hold opposite to the eye a circular ring or disk 
like a piece of coin, it will appear as a complete circle 
when it is at right angles to the axis of vision, but when 
oblique to that axis it will be projected into an ellipse 



250. How is the ring divided by large telescopes? State the 
several dimensions of Saturn and his rings. Describe the 
figure. How is the ring inferred to be a solid opake sub- 
stance 1 In what time does Saturn revolve on his axis ? What 
figure does this give to the planet ? What kind of telescope is 
required to see the phenomena of Saturn to advantage 1 



196 THE PLANETS. 

more and more flattened as its obliquity is increased, 
until, when its plane coincides with the axis of vision, 
it is j)rojected into a straight line. Let us place on the 
table a lamp to represent the sun, and holding the ring 
at a certain distance inclined a little towards the lamp, 
let us carry it round the lamp always keeping it parallel 
to itself. During its revolution it will twice present its 
edge to the lamp at opposite points, and twice at places 
90° distant from those points, it will present its broadest 
face towards the lamp. At intermediate points, it will 
exhibit an ellipse more or less open, according as it is 
nearer one or the other of the preceding positions. It 
will be seen also that in one half of the revolution the 
lamp shines on one side of the ring, and in the other 
half of the revolution on the other side. Such would 
be the successive appearances of Saturn's ring to a spec- 
tator on the sun ; and since the earth is, in respect to 
so distant a body as Saturn, ver}^ near the sun, these 
appearances are presented to us in nearly the same man- 
ner as though we viewed them from the sun. Accord 
dingly, we sometimes see Saturn's ring under the form 
of a broad ellipse, which grows continually more and 
more acute until it passes into a line, and we either lose 
sight of it altogether, or by the aid of the most power- 
ful telescopes, we see it as a fine thread of light drawn 
across the disk and projecting out from it on each side. 
As the whole revolution occupies 30 years, and the edge 
is presented to the sun twice in the revolution, this last 
phenomenon, namely, the disappearance of the ring, 
takes place every 15 years. 

252. The learner may perhaps gain a clearer idea of 
the foregoing appearances from the following diagram : 

Let A, B, C, &c. represent successive positions of Sat- 
urn and his ring in different parts of his orbit, while 



251. How is the position of the ring with respect to itself 
in all parts of its revolution ? How may the various appear- 
ances of the ring be represented ? 



197 



abc represents the orbit of the earth.* Were the ring 
when at C and G perpendicular to the CG, it would be 
seen by a spectator situated at a ov da perfect circle, 
but being inclined to the line of vision 28"^ 4', it is pro- 
jected into an ellipse. This ellipse contracts in breadth 



46. 




as the ring passes towards its nodes at A and E, where 
it dwindles into a straight line. From E to G the ring 
opens again, becomes broadest at G, and again contracts 
till it becomes a straight hne at A, and from this point 
expands till it recovers its original breadth at C. These 
successive appearances are all exhibited to a telescope of 
moderate powers. The ring is extremely thin, since the 
smallest satellite, when projected on it, more than covers 
it. The thickness is estimated at 100 miles. 

253. Saturrts ring shines wholly hy reflected light 
derived from the sun. This is evident from the fact, 
that that side only which is turned towards the sun is 
enlightened ; and it is remarkable, that the illumination 
of the ring is greater than that of the planet itself, but 



252. Explain the revolution of the ring by figure 46. 

253. Whence does the ring derive its light ? What causes 
occasion the disappearance of the ring ? At what intervals 
do these disappearances occur ? 



* It may be remarked by the learner, that these orbits are made so 
elliptical, not to represent the eccentricity of either the earth's or Sat- 
urn's orbit, but merely as the projection of circles seen very obliquely. 
17* 



19S THE PLANETS. 

the outer ring is less bright than the inner. Although, 
as we have already remarked, we view Saturn's ring 
nearly as though we saw it from the sun, yet the plane 
of the ring produced may pass between the earth and 
the sun, in which case also the ring becomes invisi- 
ble, the illuminated side being wholly turned from us. 
Thus when the ring is approaching its node at E, a spec- 
tator at a would have the dark side of the ring presented 
to him. The ring was invisible in 1833, and will be 
invisible again in 1847. The northern side of the ring 
will be seen until 1845, when the southern side will 
come into view. 

It appears, therefore, that there are three causes for 
the disappearance of Saturn's ring ; first, when the edge 
of the ring is presented to the sun ; secondly, when the 
edge is presented to the earth ; and thirdly, when the un- 
illuminated side is towards the earth. 

254. SaturrCs ring revolves in its own plane in about 
lOi hours, (lOh. 32m. 15s.4). La Place inferred this 
from the doctrine of universal gravitation. He proved 
that such a rotation was necessary, otherwise the matter 
of which the ring is composed would be precipitated 
upon its primary. He showed that in order to sustain 
itself, its pei iod of rotation must be equal to the time of 
revolution of a satellite, circulating around Saturn at a 
distance from it equal to that of the middle of the ring, 
which period would be about lOi hours. By means of 
spots in the ring, Dr. Herschel followed the' ring in its 
rotation, and actually found its period to be the same as 
assigned by La Place, — a coincidence which beautifully 
exemplifies the harmony of truth. 

255. Although the rings are very nearly concentric with 
the planet, yet recent measurements of extreme delicacy 



254. In what time does the ring revolve in its own plane ? 
How was this revolution inferred to exist before it was actually 
observed? 



SATURN. 199 

have demonstrated, that the coincidence is not mathe- 
matically exact, but that the center of gravity of the rings 
describes around that of the body a very minute orbit. 
This fact, unimportant as it may seem, is of the utmost 
consequence to the stability of the system of rings. Sup- 
posing them mathematically perfect in their circular form, 
and exactly concentric with the planet, it is demonstrable 
that they would form (in spite of their centrifugal force) 
a system in a state of unstable equilibrium, which the 
slightest external power would subvert — not by causing 
a rupture in the substance of the rings — but by precip- 
itating them unbroken on the surface of the planet. 
The ring may be supposed of an unequal breadth in its 
different parts, and as consisting of irregular solids, 
whose common center of gravity does not coincide with 
the center of the figure. Were it not for this distribu- 
tion of matter. Its equihbrium would be destroyed by 
the slightest force, such as the attraction of a satellite, 
and the ring would finally precipitate itself upon the 
planet. 

As the smallest difference of velocity between the 
planet and its rings must infallibly precipitate the rings 
upon the planet, never more to separate, it follows either 
that their motions in their common orbit round the sun, 
must have been adjusted to each other by an external 
power, with the minutest precision, or that the rings 
must have been formed about the planet while subject 
to their common orbitual motion, and under the full and 
free influence of all the acting forces. 

The rings of Saturn must present a magnificent spec- 
tacle from those regions of the planet which lie on their 
enlightened sides, appearing as vast arches spanning the 
sky from horizon to horizon, and holding an invariable 
situation among the stars. On the other hand, in the 
region beneath the dark side, a solar echpse of 15 years 



255. Are the rings concentric with the planet 1 What ad- 
vantage results from this arrangement ? How must the rings 
appear when seen from the planets ? 



200 THE PLANETS. 

in duration, under their shadow, must afford (to our 
ideas) an inhospitable abode to animated beings, but ill 
compensated by the full light of its satellites. But we 
shall do wTong to judge of the fitness or unfitness of 
their condition from what we see around us, when, per- 
haps, the very combinations w^hich convey to our minds 
only images of horror may he in reality theatres of the 
most striking and glorious displays of beneficent con- 
trivance. (Sir J. Herschel.) 

256. Saturn is attended by seven satellites. Although 
bodies of considerable size, their great distance prevents 
their being visible to any telescopes but such as afford a 
strong light and high magnifying powers. The outer- 
most satelhte is distant from the planet more than 30 
times the planet's diameter, and is by far the largest of 
the whole. It is the only one of the series whose theory 
has been investigated further than suffices to verify Kep- 
ler's law of the periodic times, which is found to hold 
good here as well as in the system of Jupiter. It ex« 
hibits, like the satellites of Jupiter, periodic variations of 
light, which prove its revolution on its axis in the time 
of a sidereal revolution about Saturn. The next satellite 
in order, proceeding inwards, is tolerably conspicuous ; 
the three next are very minute, and require pretty pow- 
erful telescopes to see them ; while the two interior sat- 
ellites, which just skirt the edge of the ring, and move 
exactly in its plane, have never been discovered but with 
the most powerful telescopes which human art has yet 
constructed, and then only under peculiar circumstances. 
At the time of the disappearance of the rings (to ordinary 
telescopes) they were seen by Sir William Herschel 
with his great telescope, projected along the edge of the 
ring, and threading like beads the thin fibre of light to 



256. What is the number of Saturn's satellites ? How far 
distant from the planet is the outermost satellite ? Do the sat- 
eUites follow Kepler's third law ? Which of the satellites are 
easily seen ? Do they undergo eclipses ? 



URANUS. 201 

which the ring is then reduced. Owing to the obliquity 
of the ring, and of the orbits of the satellites to that of 
their primary, there are no eclipses of the satellites, the 
two interior ones excepted, until near the time when the 
ring is seen edgewise. 

257. Uranus is the remotest planet belonging to our 
system, and is rarely visible except to the telescope. Al- 
though his diameter is more than four times that of the 
earth, (35,112 miles.) yet his distance from the sun is 
likewise nineteen times as great as the earth's distance, 
or about 1,800,000,000 miles. His revolution around 
the sun occupies nearly 84 years, so that his position in 
the heavens for several years in succession is nearly sta- 
tionary. His path lies very nearly in the echptic, being 
inclined to it less than one degree, (46^ 28'^44.) 

The sun himself when seen from Uranus dwindles al- 
most to a star, subtending as it does an angle of only 
V 40" ; so that the surface of the sun would appear 
there 400 times less than it does to us. 

This planet was discovered by Sir William Herschel 
on the 13th of March 1781. His attention was attracted 
to it by the largeness of its disk in the telescope ; and 
finding that it shifted its place among the stars, he at 
first took it for a comet, but soon perceived that its orbit 
was not eccentric like the orbits of comets, but nearly 
circular like those of the planets. It was then recog- 
nized as a new member of the planetary system, a con- 
clusion which has been justified by all succeeding ob- 
servations. 

258. Uranus is attended by six satellites. So minute 
objects are they, that they can be seen only by powerful 
telescopes. Indeed, the existence of more than two is 
still considered as somewhat doubtful These two, 



257. Uranus. — State his diameter — distance from the sun — 
periodic time — inclination of his orbit. How would the sun 
appear from Uranus ? State the history of his discovery^ 



202 THE PLANETS. 

however, offer remarkable, and indeed quite unexpected 
and unexampled peculiarities. Contrary to the unbro- 
ken analogy of the whole planetary system, the planes 
of their orbits are nearly perpendicular to the ecliptic^ 
being inclined no less than 78° 58^ to that plane, and in 
these orbits their motions are retrograde ; that is, instead 
of advancing from west to east around their primary, as 
is the case with all the other planets and satellites, they 
move in the opposite direction. With this exception, all 
the motions of the planets, whether around their own 
axes, or around the sun, are from west to east. The sun, 
himself, turns on his axis from west to east ; all the pri- 
mary planets revolve around the sun from west to east ; 
their revolutions on their own axes are also in the same 
direction ; all the secondaries, with the single exception 
above mentioned, move about their primaries from west 
to east ; and, finally, such of the secondaries as have 
been discovered to have a diurnal revolution, follow the 
same course. Such uniformity among so many motions, 
could have I'esulted only from forces impressed upon 
them by the same omnipotent hand ; and few things in 
the creation more distinctly proclaim that God made the 
world. 

THE NEW PLANETS, CERES, PALLAS, JUNO, AND VESTA. 

259. The commencement of the present century was 
rendered memorable in the annals of astronomy, by the 
discovery of four new planets between Mars and Jupiter. 
Kepler, from some analogy which he found to subsist 
among the distances of the planets from the sun, had 
long before suspected the existence of one at this dis- 
tance ; and his conjecture was rendered more probable 
by the discovery of Uranus, which follows the analogy 



258. By how many satellites is Uranus attended ^ What is 
said of their minuteness ? What remarkable peculiarities have 
they? In what direction are the motions of all the bodies in 
the solar system ? What does this fact indicate with respect to 
their origin ? 



NEW PLANETS. 203 

of the other planets. So strongly, indeed, were astrono- 
mers impressed with the idea that a planet would be 
found between Mars and Jupiter, that, in the hope of 
discovering it, an association was formed on the conti 
nent of Europe of twenty-four observers, who divided 
the sky into as man}^ zones, one of which was allotted 
to^each member of the association. The discovery of 
the first of these bodies was however made accidentally 
by Piazzi, an astronomer of Palermo, on the first of Jan- 
uary, 1801. It was shortly afterwards lost sight of on 
account of its proximity to the sun, and was not seen 
again until the close of the year, when it was re-discov- 
ered in Germany. Piazzi called it Ceres, in honor of 
the tutelary goddess of Sicily ; and her emblem, the 
sickle ? , has been adopted as its appropriate symbol. 

The difficulty of finding Ceres induced Dr. Olbers, of 
Bremen, to examine with particular care all the small 
stars that lie near her path, as seen from the earth ; and 
while prosecuting these observations, in March, 1802, he 
discovered another similar body, very nearly at the same 
distance from the sun, and resembling the former in 
many other particulars. The discoverer gave to this se- 
cond planet the name of Pallas, choosing for its symbol 
the lance $ , the characteristic of Minerva. 

260. The most surprising circumstance connected 
with the discovery of Pallas, was the existence of two 
planets at nearly the same distance from the sun, and 
apparently having a common node. On account of this 
singularity. Dr. Olbers was led to conjecture that Ceres 
and Pallas are only fragments of a larger planet, which 
had formerly circulated at the same distance, and been 
shattered by some internal convulsion. The hypothesis 
suggested the probability that there might be other frag- 



259. Name the New Planets. When were they discovered ? 
What had been conjectured previous to their discovery ? Who 
discovered the first ? What is its name ? How was Pallas dis- 
covered ? 



204 THE PLANETS. 

ments, whose orbits, however they might differ in ec- 
centricity and incHnation, might be expected to cross the 
ecHptic at a common point, or to have the same node. 
Dr. Olbers, therefore, proposed to examine carefully every 
month, the two opposite parts of the heavens in which 
the orbits of Ceres and Pallas intersect one another, with 
a view to the discovery of other planets, which might 
be sought for in those parts with greater chance of suc- 
cess than in a wider zone, embracing the entire limits 
of these orbits. Accordingly, in 1804, ne^r one of the 
nodes of Ceres and Pallas, a third planet was discovered. 
This was called Juno, and the character 5 was adopted 
for its symbol, representing the starry sceptre of the 
queen of Olympus. Pursuing the same researches, in 
1807, a fourth planet was discovered, to which was 
given the name of Vesta, and for its symbol the char- 
acter fi was chosen — an altar surmounted with a censer 
holding the sacred fire. 

After this historical sketch, it wall be sufficient to clas- 
sify under a few heads the most interesting particulars 
relating to the New Planets. 

261. The average distance of these bodies from the 
sun is 261,000,000 miles ; and it is remarkable that 
their orbits are very near together. Taking the distance 
of the earth from the sun for unity, their respective dis- 
tances are 2.77, 2.77, 2.67, 2.37. 

As they are found to be governed, like the other mem- 
bers of the solar system, by Kepler's law, that regulates 
the distances and times of revolution, their periodical 
times are of course pretty nearly equal, averaging about 
4^ years. 

In respect to the inclination of their orbits, there is 
considerable diversity. The orbit of Vesta is inclined 



260. How do Ceres and Pallas compare in distance from the 
sun and the place of their nodes ? What hypothesis did Olbera 
adopt ? State the circumstances connected with the discovery 
of Juno and Vesta, 



MOTIONS OF THE PLANETARY SYSTEM. 205 

to the ecliptic only about 7°, while that of Pallas is more 
than 34"^. They all therefore have a higher inclination 
than the orbits of the old planets, and of course make 
excursions from the ecliptic beyond the limits of the 
Zodiac. 

The eccentricity of their orhits is also, in general, 
greater than that of the old planets ; and the eccentrici- 
ties of the orbits of Pallas and Juno exceed that of the 
orbit of Mercury. 

Their small size constitutes one of their most remark- 
able peculiarities. The difficulty of estimating the ap- 
parent diameters of bodies at once so very small and so 
far off, would lead us to expect diiferent results in the 
actual estimates. Accordingly, while Dr. Herschel es- 
timates the diameter of Pallas at only 80 miles, Schroe- 
ter places it as high as 2,000 miles, or about the size of 
the moon. The volume of Vesta is estimated at only 
one fifteen thousandth part of the earth's, and her surface 
is only about equal to that of the kingdom of Spain. 
These little bodies are surrounded by atmospheres of 
great extent, some of which are uncommonly luminous, 
and others appear to consist of nebulous or vapory mat- 
ter. These planets in general shine with a more vivid 
light than might be expected from their great distance 
and diminutive size. 



CHAPTER IX. 

MOTIONS OF THE PLANETARY SYSTEM QUANTITY OF MAT- 
TER IN THE SUN AND PLANETS STABILITY OF THE SO- 
LAR SYSTEM. 

262. We have waited until the learner may be sup- 
posed to be familiar v/ith the contemplation of the heav- 

361, What is the average distance of the New Planets from 
the sun ? How do these orbits lie with respect to each other? 
Are they subject to Kepler's third law ? What is their average 
periodical time ? What is said of the inclination of their or- 
bits ? Also, of the eccentricity ? What is their size ? 
18 



206 THE PLANETS. 

enly bodies, individually, before inviting his attention to 
a systematic view of the planets, and of their motions 
around the sun. The time has now arrived for entering 
more advantageously upon this subject, than could have 
been done at an earlier period. 

There are two methods of arriving at a knowledge of 
the motions of the heavenly bodies. One is to begin 
with the apparent, and from these to deduce the real 
motions ; the other is, to begin with considering things 
as they really are in nature, and then to inquire why 
they appear as they do. The latter of these methods is 
by far the more eligible ; it is much easier than t1ie 
other, and proceeding from the less difficult to that which 
is more difficult, from motions that are very simple to 
such as are complicated, it finally puts the learner in pos- 
session of the whole machinery of the heavens. We 
shall, in the first place, therefore, endeavor to introduce 
the learner to an acquaintance with the simplest motions 
of the planetary system, and afterwards to conduct him 
gradually through such as are more complicated and dif- 
ficult. 

263. Let us first of all endeavor to acquire an adequate 
idea of absolute space, such as existed before the crea- 
tion of the world. We shall find it no easy matter to 
form a correct notion of infinite space ; but let us fix our 
attention, for some time, upon extension alone, devoid of 
every thing material, without light or life, and without 
bounds. Of such a space we could not predicate the 
ideas of up or down, east, west, north, or south, but all 
reference to our own horizon (which habit is the most 
difficult of all to eradicate from the mind) must be com- 
pletely set aside. Into such a void we would introduce 
the Sun. We would contemplate tliis body alone, in 
the midst of boundless space, and continue to fix the at- 



262. What are the two methods of studying the motions of 
the heavenly bodies \ Which method is best ? What motions 
will be first considered ? 



MOTIONS OF THE PLANETARY SYSTEM. 207 

tention upon this object, until we had fully settled its 
relations to the surrounding void. The ideas of up and 
down would now present themselves, but as yet there 
would be nothing to suggest any notion of the cardinal 
points. We suppose ourselves next to be placed on the 
surface of the sun, and the firmament of stars to be 
lighted up. The slow revolution of the sun on his axis, 
would be indicated by a corresponding movement of the 
stars in the opposite direction ; and in a period equal to 
more than 25 of our days, the spectator would see the 
heavens perform a complete revolution around the sun, 
as he now sees them revolve around the earth once in 
24 hours. The point of the firmament where no mo- 
tion appeared, would indicate the position of one of the 
poles, which being called North, the other cardinal points 
w^ould be immediately suggested. 

Thus prepared, we may now enter upon the conside- 
ration of the planetary motions. 

264. Standing on the sun, we see all the planets mo- 
ving slowly around the celestial sphere, nearly in the 
same great highway, and in the same direction from 
west to east. They move, however, with very unequal 
velocities. Mercury makes very perceptible progress 
from night to night, like the moon revolving about the 
earth, his daily progress eastward being one third as 
great as that of the moon, since he completes his entire 
revolution in about three months. If we watch the 
course of this planet from night to night, we observe it, 
in its revolution, to cross the ecliptic in two opposite 
points of the heavens, and wander about 7° from that 
plane at its greatest distance from it. Knowing the po- 
sition of the orbit of Mercury with respect to the ecliptic, 
we may now, in imagination, represent that orbit by a 



263. How can we form a correct idea of absolute space ? 
What can we predicate of such a space 1 If the sun were pla- 
ced in such a void, what new ideas would present themselves ? 
How should we get a knowledge of the cardinal points ? 



208 THE PLANETS. 

great circle passing through the center of the planet and 
the center of the sun, and cutting the plane of the eclip- 
tic in two opposite points at an angle of 7°. We may 
imagine the intersection of these two great circles with 
the celestial vault to be marked out in plain and palpa- 
ble lines on the face of the sky ; but we must bear in 
mind that these orbits are mere mathematical planes, 
having no permanent existence in nature, any more than 
the path of an eagle flying through the sky ; and if we 
conceive of their orbits marked on the celestial vault, 
we must be careful to attach to the representation the 
same notion as to a thread or wire, carried round to trace 
out the course pursued by a horse in a race-ground.* 

The planes of both the ecliptic and the orbit of Mer- 
cury, may be conceived of as indefinitely extended to a 
great distance until they meet the sphere of the stars ; 
but the lines which the earth and Mercury describe in 
those planes, that is, their orbits may be conceived of as 
comparatively near to the sun. Could w^e now for a 
moment be permitted to imagine that the planes of the 
ecliptic, and of the orbit of Mercury, were made of thin 
plates of glass, and that the paths of the respective plan- 
ets w^ere marked out on their planes in distinct lines, we 
should perceive the orbit of the earth to be almost a per- 
fect circle, while that of Mercury would appear distinctly 
elliptical. But having once made use of a palpable sur- 



264. Where must the spectator be placed in order to see the 
real motions of the planets ? How would the motions oi' the 
several planets appear from this station? State the particular 
movements of Mercury. How may we imagine the ecliptic 
and the orbit of Mercury to be represented on the sky ? How 
shall we conceive of \\\e planes o{ these orbits as distinguished 
from the orbit itself? 



* It would seem superfluous to caution the reader on so plain a point, 
did not the experience of the instructor constantly show that young 
learners, from the habit of seeing the celestial motions represented in 
orreries and diagrams, almost always fall into the absurd notion of con- 
sidering the orbits of the planets as having a distinct and indep(^ndent 
existence. 



MOTIONS OF THE PLAXETARY SYSTEM. 209 

face and visible lines to aid us in giving position and fig- 
ure to the planetary orbits, let us now throw aside these 
devices, and hereafter conceive of these planes and or- 
bits as they are in nature, and learn to refer a body to a 
mere mathematical plane, and to trace its path in that 
plane through absolute space. 

265. A clear understanding of the motions of Mercury 
and of the relation of its orbit to the plane of the echp- 
tic, will render it easy to understand the same particulars 
in regard to each of the other planets. , Standing on the 
sun we should see each of the planets pursuing a similar 
course to that of Mercury, all moving from west to east, 
with motions differing from each other chiefly in tw^o re- 
spects, namely, in their velocities, and in the distances 
to which they ever recede from the ecliptic. 

The earth revolves about the sun very much like Ye- 
nus, and to a spectator on the sun, the motions of these 
two planets would exhibit much the same appearances. 
We have supposed the observer to select the plane of 
the earth's orbit as his standard of reference, and to see 
how each of the other orbits is related to it ; but such a 
selection of the ecliptic is entirely arbitrary ; the specta- 
tor on the sun, who views the motions of the planets as 
they actually exist in nature, would make no such dis- 
tinction between the different orbits, but merely inquire 
how they were mutually related to each other. Taking, 
however, the ecliptic as the plane to which all the others 
are referred, we do not, as in the case of the other plan- 
ets, inquire how its plane is inclined, nor what are its 
nodes, since it has neither inclination nor node. 

268. The attempt to exhibit the motions of the solar 
system, and the positions of the planetary orbits by 



26.5, If we stood on the sim, how should we see each of the 
planets revolve 1 Why is the earth's orbit selected as the stan- 
dard of reference 1 Would the spectator on the sun make any 
such distinction ? 

18^ 



210 THE PLANETS. 

means of diagrams, or even orreries, is usually a failure 
The student who relies exclusively on such aids as 
these, wdll acquire ideas on this subject that are both in- 
adequate and erroneous. They may aid reflection, but 
can never supply its place. The impossibihty of rep- 
resenting things in their just proportions will be evident 
when we reflect, that to do this, if, in an orrery, we 
make Mercury as large as a cherry, we should require to 
represent the sun by a globe six feet in diameter. If we 
preserve the same proportions in regard to distance, we 
must place Mercury 250 feet, and Uranus 12,500 feet, 
or more than two miles from the sun. The mind of the 
student of astronomy must, therefore, raise itself from 
such imperfect representations of celestial phenomena as 
are afforded by artificial mechanism, and, transferring his 
contemplations to the celestial regions themselves, he 
must conceive of the sun and planets as bodies that bear 
an insignificant ratio to the immense spaces in which 
they circulate, resembling more a few little birds flying 
in the open sky, than they do the crowded machinery of 
an orrery. 

267. Having acquired as correct an idea as we are 
able of the planetary system, and of the positions of the 
orbits with respect to the ecliptic, let us next inquire 
into the nature and causes of the apparent motions. 

Tlie apparent motions of the planets are exceedingly 
unlike the real motions, a fact which is owing to two 
causes ; first, M;e view them out of the center of their or- 
bits ; secondly, ice are ourselves in motion. From the 
first cause, the apparent places of the planets are greatly 
changed by perspective ; and from the second cause, 



266. What is said of the attempt to represent the positions 
and motions of the solar system by diagrams and orreries ? 
Give examples. 

267. Are the apparent motions of the planets like the real 
motions ? What makes them different ? How does each cause 
operate ? What is the heliocentric place, and what the geo- 
centric place of a planet ? 



MOTIONS OF THE PLANETARY SYSTEM. 211 

we attribute to the planets changes of place which arise 
from our own motions of which we are unconscious. 

The situation of a heavenly body as seen from the 
center of the sun is called its heliocentric place ; as seen 
from the center of the earth, its geocentric place. The 
geocentric motions of the planets must, according to 
what has just been said, be far more irregular and com- 
plicated than the heliocentric. 

268. The apparent motions of the Inferior Planets as 
seen from the earth, have been already explained in ar- 
ticles 216 and 217 ; from which it appeared, that Mer- 
cury and Venus move backwards and forwards across 
the sun, the former never being seen farther than 29° 
and the latter never more than 47° from that luminary. 
It was also shown that while passing from the greatest 
elongation on one side to the greatest elongation on the 
other side, through the superior conjunction, the apparent 
motions of these planets are accelerated by the motion 
of the earth ; but that while moving through the infe- 
rior conjunction, at which time their motions are retro- 
grade, they are apparently retarded by the earth's mo- 
tion. Let us now see what are the geocentric motions 
of the Superior Planets. 

269. Let A, B, C, (Fig. 47,) represent the earth in 
different positions in its orbit, and M a superior planet as 
Mars, and NR an arc of the concave sphere of the 
heavens. First, suppose the planet to remain at rest in 
M, and let us see what apparent motions it will receive 
from the real motions of the earth. When the earth is 
at B, it will see the planet in the heavens at N ; and as 
the earth moves successively through, C, D, E, F, the 
planet will appear to move through O, P, Q,, R. B and 
F ai'e the two points of greatest elongation of the earth 
from the sun as seen from the planet ; hence between 



268. Describe the apparent motions of Mercury and Venus 
from figure 40. 



212 



THE PLANETS. 



these two points, while passing through the part of her 
orbit most remote from the planet, (when the planet is 
seen in superior conjunction,) the earth by her own mo- 
Fig. 47. 




tion gives an apparent motion to the planet in the order 
of the signs — that is, the apparent motion given by the 
earth is direct. But in passing from F to B through A, 
when the planet is seen in opposition, the apparent mo- 
tion given to the planet by the earth's motion is from R 
to N, and is therefore retrograde. As the arc described 
by the earth, when the motion is direct, is much greater 
than when the motion is retrograde, while the apparent 
arc of the heavens described by the planet from N toR 
in the one case, and from R to N in the other, is the 



269. Describe the motions of the Superior Planets from fig- 
ure 47. The planet remaining at rest, what apparent motions 
will the motion of the earth impart to it, when in opposition ? 
What when in superior conjunction ? 



J 



MOTIONS OF THE PLANETARY SYSTEM. 213 

same in both cases, the retrograde motion is much swifter 
than the direct, being performed in much less time. 

270. But the superior planet is not in fact at rest, as 
we have supposed, but is all the while moving east- 
ward, though with a slower motion than the earth. In- 
deed, A\ath respect to the remotest planets as Saturn and 
Uranus, the forward motion is so exceedingly slow that 
the above representation is nearly true for a single year. 
Still, the eftect of the. real motions of all the superior 
planets eastward, is to increase the direct apparent mo- 
tion communicated by the earth and to diminish the ret- 
rograde motion. 

If Mars stood still while the earth went round the 
sun, then a second opposition as at A, would occur at 
the end of one year from the first ; but while the earth 
is performing this circuit. Mars is also moving the same 
way, more than half as fast, so that when the earth re- 
turns to A, the planet has already performed more than 
half the same circuit, and vnll have completed its whole 
revolution before the earth comes up with it. Indeed, 
Mars, after having been once seen in opposition, does not 
come into opposition again until after two years and 
fifty days. And since the planet is then comparatively 
very near to us, and appears very large and bright, rising 
unexpectedly about the time the sun sets, he surprises 
the world as though it were some new celestial body. 
But on account of the slow progress of Saturn and Ura- 
nus, we find after having performed one circuit around 
the sun, that they are but httle advanced beyond where 
we left them at the last opposition. The time between 
one opposition of Saturn and another is only a year and 
thirteen days. 

It appears, therefore that the superior planets steadily 
pursue their course around the sun, but that their appar- 



270. How does the real motion of the planet modify the fore- 
going results ? How in respect to the remotest planets, as Ura- 
nus, and how in respect to a nearer planet as Mars ? How 
often is Mars in opposition ? What is his appearance then ? 



214 THE PLANETS. 

ent retrograde motion when in opposition, is occasioned 
■ by our passing by them with a swifter motion, like the 
apparent backward motion of a vessel when we over- 
take it and pass rapidly by it in a steamboat. 

QUANTITY OF MATTER IN THE SUN AND PLANETS. 

271. It would seem at first view very improbable that 
an inhabitant of this earth should be able to weigh the 
sun and planets, and estimate the exact quantity of mat- 
ter which they severally contain. But the principles of 
Universal Gravitation conduct us to this result, by a 
process remarkable for its simplicity. By comparing the 
relations of a few elements that are known to us, we 
ascend to the knowledge of such as appeared to be be- 
yond the pale of human investigation. We learn the 
quantity of matter in a body from the force of gravity 
it exerts, and this force is estimated by its effects. 
Hence worlds are weighed with as much ease as a peb- 
ble or an article of merchandise. 

272. The sun contains about 355,000 times as much 
matter as the earth, and 800 times as much matter as all 
the planets. This however, is owing rather to its great 
size than to the specific gravity of its materials, for the 
density of the sun is only one fourth as great as that of 
the earth. The earth is nearly 5^ times as heavy as 
water, but the sun is only a little heavier than that fluid. 
The planets near the sun are in general more dense than 



271. What is said of the apparent difficulty of weighing the 
sun and planets ? What great principles lead us to this re- 
sult 1 How do we learn the quantity of matter in the bodies 
of the solar system ? 

272. How much more matter does the sun contain than the 
earth ? How much more than all the planets ? What is the 
density of the sun compared with that of the earth ? How 
much heavier is the earth than water ? How much heavier is 
the sun than water 1 Which of the planets have the greatest 
density 1 How heavy is Mercury ? How heavy is Saturn ? 



STABILITY OF THE SOLAR SYSTEM. 215 

those more remote ; Mercury being heavier than lead, 
while Saturn is as light as a cork. The decrease in 
density however, is not entirely regular, since Yenus is 
a httle lighter than the earth, while Jupiter is heavier 
than Mars, and Uranus than Saturn. 

STABILITY OF THE SOLAR SYSTEM. 

273. The perturbations occasioned by the motions of 
the planets by their action on each other are very nu- 
merous, since every body in the system exerts an attrac- 
tion on every other, in conformity with the law of Uni- 
versal Gravitation. Venus and Mars, approaching as 
they do at times comparatively near to the earth, sen- 
sibly disturb its motions, and the satelhtes of the re- 
moter planets greatly disturb each other's movements. 

274. The derangement which the planets produce in 
the motion of one of their number will be very small in 
the course of one revolution ; but this gives us no secu- 
rity that the derangement may not become very large 
in the course of many revolutions. The cause acts per- 
petually, and it has the whole extent of time to work in. 
Is it not easily conceivable then, that in the lapse of ages, 
the derangements of the motions of the planets may 
accumulate, the orbits may change their form, and their 
mutual distances may be much increased or diminished ? 
Is it not possible that these changes may go on without 



273. What is said of the perturbations occasioned by the ac- 
tion of the planets on each other ? Which planets in particu- 
lar, disturb the motions of the earth ? 

274. How is the derangement produced by the planets upon 
any one of them, in a single revolution 1 What may be the 
ultimate effect of these disturbing forces ? What would be 
the consequence of increasing the eccentricity of the earth's 
orbit — or of bringing the moon nearer the earth — or of alter- 
ing the positions of the planets with respect to that of the 
earth? What changes are actually going on in the motions 
of the heavenly bodies 1 



216 THE PLANETS. 

limit, and end in the complete subversion and ruin of the 
system? If, for instance, the result of this mutual 
gravitation should be to increase considerably the eccen- 
tricity of the earth's orbit, or to make the moon approach 
continually nearer and nearer to the earth at every revo- 
lution, it is easy to see that in the one case, our year 
would change its character, producing a far greater ir- 
regularity in the distribution of the solar heat : in the 
other, our satellite must fall to the earth, occasioning a 
dreadful catastrophe. If the positions of the planetary 
orbits with respect to that of the earth, were to change 
much, the planets might sometimes come very near us, 
and thus increase the effect of their attraction beyond cal- 
culable limits. Under such circumstances we might have 
years of unequal length, and seasons of capricious tem- 
perature ; planets and moons of portentous size and as- 
pect glaring and disappearing at uncertain intervals ; tides 
like deluges sweeping over whole continents ; and, per- 
haps, the collision of two of the planets, and the conse- 
quent destruction of all organization on both of them. 
The fact really is, that changes are taking place in the 
motions of the heavenly bodies, which have gone on 
progressively from the first dawn of science. The ec- 
centricity of the earth's orbit has been diminishing from 
the earliest observations to our times. The moon has 
been moving quicker from the time of the first recorded 
eclipses, and is now in advance by about four times her 
own breadth, of what her own place would have been if 
it had not been aflTected by this acceleration. The ob- 
liquity of the ecliptic also, is in a state of diminution, 
and is now about two fifths of a degree less than it was 
in the time of Aristotle. (Whewell, in the Bridgewater 
Treatises, p. 128.) 

275. But amid so many seeming causes of irregular- 
ity, and ruin, it is worthy of grateful notice, that effec- 
tual provision is made for the stability of the solar sys- 
tem. The full confirmation of this fact, is among the 
grand results of Physical Astronomy. Newton did not 
undertake to demonstrate either the stability or insla- 



STABILITY OF THE SOLAR SYSTEM. 217 

bility of the system. The decision of this point re- 
quired a great number of preparatory steps and simplifi- 
cations, and such progress in the invention and improve- 
ment of mathematical methods, as occupied the best 
mathematicians of Europe for the greater part of the 
last century. Towards the end of that time, it was 
shown by La Grange and La Place, that the arrange- 
ments of the solar system are stable ; that, in the 
long run, the orbits and motions remain unchanged ; 
and that the changes in the orbits, which take place in 
shorter periods, never transgress certain very moderate 
limits. Each orbit undergoes deviations on this side 
and on that side of its average state ; but these devia- 
tions are never very great, and it finally recovers from 
them, so that the average is preserved. The planets 
produx^e perpetual perturbations in each other's motions, 
but these perturbations are not indefinitely progressive, 
but periodical, reaching a maximum value and then di- 
minishing. The periods which this restoration requires 
are for the most part enormous, — not less than thou- 
sands, and in some instances millions of years. Indeed 
some of these apparent derangements, have been going" 
on in the same direction from the creation of the world. 
But the restoration is in the sequel as complete as the 
derangement ; and in the mean time the disturbance 
never attains a sufficient amount seriously to affect the 
stability of the system. (Whewell, in the Bridgewater 
Treatises, p. 128.) I have succeeded in demonstrating 
(says La Place) that, whatever be the masses of the plan- 
ets, in consequence of the fact that they all move in the 
same direction, in orbits of small eccentricity, and but 
slightly inchned to each other, their secular irregulari- 
ties are periodical and included within narrow limits ; 
so that the planetary system will only oscillate about a 



275. Is the system stable ? Did Newton prove this ? Who 
fully established this point ? Have all the inequalities of the 
planetary motions a fixed period ? How long are some of thesa 
periods ? 

19 



218 COMETS. 

mean state, and will never deviate from it except by ^ 
very small quantity. The ellipses of the planets have 
been and always will be nearly circular. The ecliptic 
will never coincide with the equator ; and the entire ex- 
tent of the variation in its inclination, cannot exceed 
three degrees. 

276. To these observations of La Place, Professor 
Whewell adds the following on the importance, to the 
stability of the solar system, of the fact that those plan- 
ets which have great masses have orbits of small eccen- 
tricity. The planets Mercury and Mars, which have 
much the largest eccentricity among the old planets, are 
those of which the masses are much the smallest. The 
mass of Jupiter is more than two thousand times that of 
either of these planets. If the orbit of Jupiter were as 
eccentric as that of Mercury, all the security for the sta- 
bihty of the system, which analysis has yet pointed out, 
would disappear. The earth and the smaller planets 
might, by the near approach of Jupiter at his perihelion, 
change their nearly circular orbits into very long ellipses, 
and thus might fall into the sun, or fly off into remote 
space. It is further remarkable that in the newly discov- 
ered planets, of which the orbits are still more eccentric 
than that of Mercury, the masses are still smaller, so that 
the same provision is established in this case also. 



CHAPTER X. 

OP COMETS. 



277. A Comet, when perfectly formed, consists of 
three parts, the Nucleus, the Envelope, and the Tail. 
The Nucleus, or body of the comet, is generally distin- 
guished by its forming a bright point in the center of 
the head, conveying the idea of a soHd, or at least of a 



276. What planets have orbits of small eccentricity ? How 
does this fact contribute to the stability of the system ? 



219 



very dense portion of matter. Though it is usually ex- 
ceedingly small when compared A^dth the other parts of 
the comet, yet it sometimes subtends an angle capable 
of being measured by the telescope. The Envelope, 
(sometimes called the comet) is a dense nebulous cover- 
ing, which frequently renders the edge of the nucleus 
so indistinct, that it is extremely difficult to ascertain its 
diameter with any degree of precision. Many comets 
have no nucleus, but present only a nebulous mass ex- 
tremely attenuated on the confines, but gradually in- 
creasing in density towards the center. Indeed there is 
a regular gradation of comets, from such as are com- 
posed merely of a gaseous or vapory medium, to those 
which have a well defined nucleus. In some instances 
on record, astronomers have detected with their tele- 
scopes small stars through the densest part of a comet. 
The Tail is regarded as an expansion or prolongation 
of the coma ; and, presenting as it sometimes does, a 
train of appaUing magnitude, and of a pale, disastrous 
light, it confers on this class of bodies, their peculiar 
celebrity. 

Fig 48. 




These several parts are exhibited in figure 48, which 
represents the appearance of the comet of 1680. 



277. Of what three parts does a comet consist ? Describe 
each. 



220 COMETS. 

278. The number of comets belonging to the solar 
system, is probably very great. Many, no doubt, escape 
observation by being above the horizon in the day time. 
Seneca mentions, that during a total eclipse of the sun, 
which happened 60 years before the Christian era, a 
large and splendid comet suddenly made its appearance, 
being very near the sun. The elements of at least 130 
have been computed, and arranged in a table for future 
comparison. Of these six are particularly remarkable, 
viz. the comets, of 1680, 1770, and 1811; and those 
which bear the names of Halley, Biela, and Encke. 
The comet of 1680, was remarkable not only for its as- 
tonishing size and splendor, and its near approach to the 
sun, but is celebrated for having submitted itself to the 
observations of Sir Isaac Newton, and for having en- 
joyed the signal honor of being the first comet whose 
elements were determined on the sure basis of math- 
ematics. The comet of 1770, is memorable for the 
changes its orbit has undergone by the action of Jupiter, 
as will be more particularly related in the sequel. The 
comet of 1811 was the most remarkable in its appear- 
ance of all that have been seen in the present century. 
It had scarcely any perceptible nucleus, but its train 

Fig. 49. 




was very long and broad, as is represented in figure 49. 
Halley's comet (the same which re-appeared in 1835) is 



COMETS. 221 

distinguished as that whose return was first successfully 
predicted, and whose orbit is best determined ; and 
Biela's and Encke's comets are well known for their 
short periods of revolution, which subject them fre- 
quently to the view of astronomers. 

279. In magnitude and brightness comets exhibit a 
great diversity. History informs us of comets so bright 
as to be distinctly visible in the day time, even at noon 
and in the brightest sunshine. Such was the comet 
seen at Rome a little before the assassination of Julius 
Caesar. The comet of 1680 covered an arc of the heav- 
ens of 97^^, and its length was estimated at 123,000,000 
miles. That of 1811, had a nucleus of only 428 miles 
in diameter, but a tail 132,000,000 miles long. Had it 
been coiled around the earth like a serpent, it would 
have reached round more than 5,000 times. Other com- 
ets are of exceedingly small dimensions, the nucleus 
being estimated at only 25 miles ; and some which are 
destitute of any perceptible nucleus, appear to the largest 
telescopes, even when nearest to us, only as a small 
speck of fog, or as a tuft of down. The majority of 
comets can be seen only by the aid of the telescope. 

The same comet, indeed, has often very different as- 
pects, at its different returns. Halley's comet in 1305 
was described by the historians of that age, as the comet 
of terrific magnitude ; {cometa liorrendcE magnitudinis ;) 
in 1456 its tail reached from the horizon to the zenith, 
and inspired such terror, that by a decree of the Pope of 
Rome, public prayers were offered up at noon-day in all 
the Catholic churches to deprecate the wrath of heaven, 
while in 1682, its tail was only 30° in length, and in 1759 



278. What is said of the number of comets 1 How many 
have been arranged in a table. Specify the six that are most 
remarkable. State particulars respecting each. 

279. What is said of the magnitude and brightness of com- 
ets ? What was the length of the comet of 1680 ? Ditto of 
1811 ? Has the same comet different aspects at different re- 
turns ? Example in Halley's comet. 

19* 



222 COMETS. 

it was visible only to the telescope, until after it had pas- 
sed the perihelion. At its recent return in 1835, the 
greatest length of the tail was about 12^. These changes 
in the appearances of the same comet, are partly owing 
to the different positions of the earth with respect to 
them, being sometimes much nearer to them when they 
cross its track than at others ; also one spectator so situ- 
ated as to see the coma at a higher angle of elevation or 
in a purer sky than another, will see the train longer than 
it appears to another less favorably situated ; but the 
extent of the changes are such as indicate also a real 
change in magnitude and brightness. 

280. The periods of comets in their revolutions 
around the sun, are equally various. Encke's comet, 
which has the shortest known period, completes its rev- 
olution in 3^ years, or more accurately, in 1208 daySij 
while that of 1811 is estimated to have a period of 3383 
years. 

281. The distances to which different comets recede 
from the sun, are also very various. While Encke's 
comet performs its entire revolution within the orbit of 
Jupiter, Halley's comet recedes from the sun to twice 
the distance of Uranus, or nearly 3600,000,000 miles. 
Some comets, indeed, are thought to go to a much 
greater distance from the sun than this, while some even 
are supposed to pass into parabolic or hyperbolic orbits, 
and never to return. 

282. Comets shine htj reflecting the light of the sun. 
In one or two instances they have exhibited distinct 
phases, althouc{h the nebulous matter with which the 
nucleus is surrounded, would commonly prevent such 



280. How are the periods of comets ? What is that of 
Encke's comet, and that of the comet of 1811 ? 

281. How are the distances of comets from the sun ? Cora- 
pare Encke's and Halley's. Do comets always return to the sun ? 



COMETS. 223 

phases from being distinctly visible, even when they 
would otherwise be apparant. Moreover, certain quali- 
ties of polarized light enable the optician to decide 
whether the light of a given body is direct or reflected ; 
and M. Arago, of Paris, by experiments of this kind on 
the light of the comet of 1819, ascertained it to be re- 
flected light. 

283. The tail of a comet usually increases very much 
as it approaches the sun ; and it frequently does not reach 
its maximum until after the periheUon passage. In re- 
ceding from the sun, the tail again contracts, and nearly 
or quite disappears before the body of the comet is en- 
tirely out of sight. The tail is frequently divided into 
two portions, the central parts, in the direction of the 
axis, being less bright than the marginal parts. In 
i744, a comet appeared which had six tails, spread out 
like a fan. 

The tails of comets extend in a direct line from the 
sun, although more or less curved, like a long quill or 
feather, being convex on the side next to the direction 
in which they are moving a figure which may result 
from the less velocity of the portions most remote from 
the sun. Expansions of the Envelope have also been 
at times observed on the side next the sun, but these 
seldom attain any considerable length. 

284. The quantity of matter in comets is exceedingly 
small. Their tails consist of matter of such tenuity that 
the smallest stars are visible through them. They can 
only be regarded as great masses of thin vapor, suscepti- 
ble of being penetrated through their whole substance by 



282. Do comets shine by direct or by reflected light ? Do 
they exhibit phases 1 How is it known that their light is re- 
flected and not direct light "? 

283. How are the tails of comets affected by being near the 
sun ? How many tails have some comets ? In what direction 
is the tail in respect to the sun ? 



224 COMETS. 

the sunbeams, and reflecting them alike from their inte- 
rior parts and from their surfaces. It appears, perhaps, 
incredible that so thin a substance should be visible by 
reflected light, and some astronomers have held that the 
matter of comets is self-luminous ; but it requires but 
very little light to render an object visible in the night, 
and a light vapor may be visible when illuminated 
throughout an immense stratum, which could not be 
seen if spread over the face of the sky like a thin cloud. 
From the extremely small quantity of matter of these 
bodies, compared with the vast spaces they cover, New- 
ton calculated that if all the matter constituting the 
largest tail of a comet, were to be compressed to the 
same density with atmospheric air, it would occupy no 
more than a cubic inch. This is incredible, but still 
the highest clouds that float in our atmosphere, must be 
looked upon as dense and massive bodies, compared with 
the filmy and all but spiritual texture of a comet. 

285. The small quantity of matter in comets is proved 
by the fact, that they have sometimes passed very near 
to some of the planets without disturbing their motions 
in any appreciable degree. Thus the comet of 1770, in 
its way to the sun, got entangled among the satellites of 
Jupiter, and remained near them four months, yet it did 
not perceptibly change their motions. The same comet 
also came very near the earth ; so near, that, had its 
mass been equal to that of the earth, it would have 
caused the earth to revolve in an orbit so much larger 
than at present, as to have increased the length of the 
year, 2h. 47m. Yet it produced no sensible effect on 
the length of the year, and therefore its mass, as is shown 
by La Place, could not have exceeded joVo of that of 
the earth, and might have been less than this to any ex- 



284. How is the quantity of matter in comets ? Of what do 
the tails consist ? Can a substance so thin shine by reflected 
light ? What opinion had Newton of the extreme tenuity of 
the material of comets' tails \ 



COMETS. 225 

tent. It may indeed be asked, what proof we nave that 
comets have any matter, and are not mere reflections of 
light. The answer is, that, ahhough they are not able 
by their own force of attraction to disturb the motions 
of the planets, yet they are themselves exceedingly dis- 
turbed by the action of the planets, and in exact con- 
formity with the laws of universal gravitation. A deli- 
cate compass may be greatly agitated by the vicinity of 
a mass of iron, while the iron is not sensibly affected by 
the attraction of the needle. 

286. By approaching very near to a large planet, a 
comet may have its orbit entirely changed.* This fact 
is strikingly exemphfied in the history of the comet of 
1770. At its appearance in 1770, its orbit was found to 
be an ellipse, requiring for a complete revolution only 
5|- years ; and the wonder was, that it had not been seen 
before, since it was a very large and bright comet. As- 
tronomers suspected that its path had been changed, and 
that it had been recently compelled to move in this short 
ellipse, by the disturbing force of Jupiter and his satel- 
htes. The French Institute, therefore, offered a high 
prize for the most complete investigation of the elements 
of this comet, taking into account any cu'cumstances 
which could possibly have produced an alteration in its 
course. By tracing back the movements of this comet 
for some years previous to 1770, it was found that, at 
the beginning of 1767, it had entered considerably within 
the sphere of Jupiter s attraction. Calculating the amount 
of this attraction from the known proximity of the two 
bodies, it was found what must have been its orbit pre- 
vious to the time when it became subject to the distm'b- 
ing action of Jupiter. The result showed that it then 



285. How is the small quantity of matter in comets proved ? 
How was this indicated by the comet of 1770 ? What did its 
quantity of matter not exceed as compared with the earth's ? 
May we not infer that they have no matter ? 



226 COMETS, 

moved in an ellipse of greater extent, having a period of 
50 years, and having its perihelion instead of its aphelion 
near Jupiter. It w^as therefore evident why, as long as 
it continued to circulate in an orbit so far from the cen- 
ter of the system, it w^as never visible from the earth. 
In January 1 767, Jupiter and the comet happened to be 
very near one another, and as both were moving in the 
same direction, and nearly in the same plane, they re- 
mained in the neighborhood of each other for several 
months, the planet being between the comet and the 
sun. The consequence was, that the comet's orbit was 
changed into a smaller ellipse, in which its revolution 
was accomplished in 5^ years. But as it was approach- 
ing the sun in 1779, it happened again to fall in with 
Jupiter. It was in the month of June, that the attrac- 
tion of the planet began to have a sensible effect ; and 
it was not until the month of October following, that 
they were finally separated. 

At the time of their nearest approach, in August, Ju- 
piter was distant from the comet only 4^y of its distance 
from the sun, and exerted an attraction upon it 225 
times greater than that of the sun. By reason of this 
powerful attraction, Jupiter being farther from the sun 
than the comet, the latter was drawn out into a new or- 
bit, which even at its perihelion came no nearer to the 
sun than the planet Ceres. In this third orbit, the comet 
requires about 20 years to accomplish its revolution ; 
and being at so great a distance from the earth, it is in- 
visible, and w^ll forever remain so, unless, in the course 
of ages, it may undergo new perturbations, and move 
again in some smaller orbit as before. 



286. How may a comet have its orbit changed ? How was 
the orbit of the comet of 1770 changed? How was this fact as- 
certained ? What action did Jupiter exert upon it in 1767, and 
again in 1779 ? How far was Jupiter from the comet at the 
time of their nearest approach ? How many years does it now 
require to perform its revolution ? 



ORBITS AND MOTIONS OF COMETS. 227 



ORBITS AND MOTIONS OF COMETS. 

287. The planets, as we have seen, (with the excep- 
tion of the four new ones, which seem to be an interme- 
diate class of bodies between planets and comets,) move 
in orbits which are nearly circular, and all very near to 
the plane of the ecliptic, and all move in the same direc- 
tion from west to east. But the orbits of comets are far 
more eccentric than those of the planets ; they are in- 
clined to the ecliptic at various angles, being sometimes 
even nearly perpendicular to it ; and the motions of 
comets are sometimes retrograde. 

288. The Elements of a comet are five, viz. (1) The 
perihelion distance; (2) longitude of the perihelion ; (3) 
longitude of the node ; (4) inclination of the orbit ; (5) 
time of the perihelion passage. 

The investigation of these elements is a problem ex- 
tremely intricate, requiring for its solution, a skilful and 
laborious apphcation of the most refined analysis. This 
difficulty arises from several circumstances pecuhar to 
comets. In the^r^^ place, from the elongated form of 
the orbits which these bodies describe, it is during only 
a very small portion of their course, that they are visible 
from the earth, and the observations made in that short 
period, cannot afterwards be verified on more convenient 
occasions ; whereas in the case of the planets, whose or- 
bits are nearly circular, and whose movements may be 
followed uninterruptedly throughout a complete revolu- 
tion, no such impediments to the determination of their 
orbits occur. In the second place, there are many com- 
ets which move in a direction opposite to the order of 
the signs in the zodiac, and sometimes nearly perpen- 
dicular to the plane of the ecliptic ; so that their appa- 



287. How do the orbits of comets differ from those of planets? 

288. What particulars are called the elements of a comet ? 
What is said of the difficulty of determining these elements 1 
Specify the several reasons of this difficulty. 



228 COMETS. 

rent course through the heavens is rendered extremely 
compHcated, on account of the contrary motion of the 
earth. In the third place, as there may be a multitude 
of elliptic orbits, whose perihelion distances are equal, 
(see p. 100,) it is obvious that, in the case of very ec- 
centric orbits, the slightest change in the position of the 
curve near the vertex, where alone the comet can be ob- 
served, must occasion a very sensible difference in the 
length of the orbit ; and therefore, though a small error 
produces no perceptible discrepancy between the ob- 
served and the calculated course, while the comet re- 
mains visible from the earth, its effect when diffused 
over the whole extent of the orbit, may acquire a most 
material or even a fatal importance. 

289. On account of these circumstances, it is found 
exceedingly difficult to lay down the path which a comet 
actually follows through the whole system, and least of 
all, possible to ascertain with accuracy, the length of the 
major axis of the ellipse, and consequently the periodical 
revolution.* An error of only a few seconds may cause 
a difference of many hundred years. In this manner, 
though Bessel determined the revolution of the comet of 
1769 to be 2089 years, it was found that an error of no 
more than 5^'' in observation, would alter the period either 
to 2678 years, or to 1692. Some astronomers, in calcula- 
ting the orbit of the great comet of 1680, have found the 
length of its greater axis 426 times the earth's distance 
from the sun, and consequently its period 8792 years ; 
whilst others estimate the greater axis 430 times the 
earth's distance, which alters the period to 8916 years. 



289. Is it easy to ascertain the major axis of a comet's orbit, 
and its periodic time ? What difference would an error of a few 
seconds occasion ? Give examples of this. 



* For when we know the length of the major axis, we can find tht 
periodic time by Kepler's law, which applies as well to comets as t« 
planets. 



MOTIONS AND ORBITS OF COMETS. 



229 



Newton and Halley, however, judged that this comet 
accomplished its revolution in only 570 years. 

290. The appearances of the same comet at different 
periods of its return are so various, that we can never 
pronounce a given comet to be the same with one that 
has appeared before, from any pecuharities in its physi- 
cal aspect. The identity of a comet wdth one already 
on record, is determined by the identity of the elements. 
It was by this means that Halley first estabhshed the 
identity of the comet w^hich bears his name, with one 
that had appeared at several preceding ages of the world, 
of which so many particulars were left on record, as to 
enable him to calculate the elements at each period. 
These were as in the follo-s^dng table. 



Time of appear. 


liiclin. of the orbit. 


Lon. of Node. 


Lon. of Per 


Per. Dist 


Course. 


1456 


17* 56' 


48^ 30' 


3Ui'' 00 


0.58 


Retrograde 


1531 


17 56 


49 25 


301 38 


0.57 


" 


1607 


17 02 


50 21 


302 16 


0.58 


" 


1682 


17 42 


50 48 


301 36 


0.58 


" 



On comparing these elements, no doubt could be en- 
tertained that they belonged to one and the same body ; 
and since the interval between the successive returns 
was seen to be 75 or 76 years, Halley ventured to pre- 
dict tha.t it would again return in 1758. Accordingly, 
the astronomers who lived at that period, looked for its 
return with the greatest interest. It w^as found, how- 
ever, that on its way towards the sun it would pass very 
near to Jupiter and Saturn, and by their action on it, it 
would be retarded for a long time. Clairaut, a distin- 
guished French mathematician, undertook the laborious 
task of estimating the exact amount of this retardation, 
and found it to be no less than 618 days, namely, 100 



290. Can we identify a comet with one that has been seen 
before, by its appearance ? How is this identity determined ? 
Hovv was Halley's comet proved to be the same with one that 
had appeared before ? How was its return predicted ? What 
causes alter the periods of its return ? 
20 



230 COMETS. 

days by the action of Jupiter, and 518 days by that of 
Saturn. This would delay its appearance until early in 
the year 1759, and Clairaut fixed its arrival at the peri- 
helion within a month of April 13th. It came to the 
perihelion on the 12th of March. 

291. The return of Ilalley's comet in 1835, was 
looked for with no less interest than in 1759. Several 
of the most accurate mathematicians of that age had cal- 
culated its elements with inconceivable labor. Their 
zeal was rewarded by the appearance of the expected 
visitant at the time and place assigned ; it travelled the 
northern sky presenting the very appearances, in most 
respects, that had been anticipated ; and came to its pe- 
rihelion on the 16th of November, within two days of 
the time predicted by Pontecoulant, a French mathe- 
matician who had, it appeared, made the most success- 
ful calculation.* On its previous return, it was deemed 
an extraordinary achievement to have brought the pre- 
diction vsdthin a month of the actual time. 

Many circumstances conspired to render this return of 
Ilalley's comet an astronomical event of transcendent 
interest. Of all the celestial bodies, its history was the 
most remarkable ; it afforded most triumphant evidence 
of the truth of "the doctrine of universal gravitation, and 
of course of the received laws of astronomy ; and it in- 
spired new confidence in the power of that instrument, 
(the Calculus,) by means of which its elements had been 
investigated. 

292. Encke's comet, by its frequent returns, (once in 
3^ years,) affords peculiar facihties for ascertaining the 



291. How was the return of Halley's comet in 1835 re- 
garded by astronomers ? What circumstances conspired to 
produce this feeling ? 

* See Professor Loomis's Observations on Halley's Comet. Amer. 
Jour. Science, 30, 209. 



ORBITS AND MOTIONS OF COMETS. 231 

laws of its revolution ; and it has kept the appointments 
made for it with great exactness. On its late return 
(1839) it exhibited to the telescope a globular mass of 
nebulous matter, resembling fog, and moved towards its 
perihelion with great rapidity. 

But what has made Encke's comet particularly fa- 
mous, is its having first revealed to us the existence of a 
Resisting Medium in the planetary spaces. It has long 
been a question, whether the earth and planets revolve 
in a perfect void, or whether a fluid of extreme rarity 
may not be diffused through space. A perfect vacuum 
was deemed most probable, because no such effects on 
the motions of the planets could be detected as indicated 
that they encountered a resisting medium. But a feather 
or a lock of cotton propelled with great velocity, might 
render obvious the resistance of a medium which would 
not be perceptible in the motions of a cannon ball. Ac- 
cordingly, Encke's comet is thought to have plainly suf- 
fered a retardation from encountering a resisting medium 
in the planetary regions. The effect of this resistance, 
from the first discovery of the comet to the present time, 
has been to diminish the time of its revolution about 
two days. Such a resistance by destroying a part of the 
projectile force, would cause the comet to approach 
nearer to the sun, and thus to have its periodic time 
shortened. The ultimate effect of this cause will be to 
bring the comet nearer to the sun at every revolution, 
until it finally falls into that luminary, although many 
thousand years will be required to produce this catas- 
trophe. It is conceivable, indeed, that the effects of 
such a resistance may be counteracted by the attraction 
of one or more of the planets, near which it may pass in 
its successive returns to the sun. 



292. Are the elements of Encke's comet calculated with ex- 
actness 1 What was its appearance in 1839 ? What has made 
it pecuUarly famous 1 Why should it be so favorable for detCfC- 
ting a resisting medium 1 What has been its effect on the 
motions of the comet ? What will be its ultimate eff*ect ? 



232 COMETS. 

293. It is peculiarly interesting to see a portion of 
matter, of a tenuity exceeding the thinnest fog, pursuing 
its path in space, in obedience to the same laws as those 
which regulate such large and heavy bodies as Jupiter 
or Saturn. In a perfect void, a speck of fog if propelled 
by a suitable projectile force, would revolve around the 
sun, and hold on its way through the widest orbit, with 
as sure and steady a pace as the heaviest and largest 
bodies in the system. 

294. Of the physical nature of comets, little is under- 
stood. It is usual to account for the variations which 
their tails undergo, by referring them to the agencies of 
heat and cold. The intense heat to which they are 
subject in approaching so near the sun as some of them 
do, is alleged as a sufficient reason for the great expan- 
sion of thin nebulous atmospheres forming their tails ; 
and the inconceivable cold to which they are subject in 
receding to such a distance from the sun, is supposed to 
account for the condensation of the same matter until it 
returns to its original dimensions. Thus the great comet 
of 1680, at its perihelion, approached 166 times nearer 
the sun than the earth, being only 130,000 miles from 
the surface of the sun. The heat which it must have 
received, was estimated to be equal to 28,000 times that 
which the earth receives in the same time, and 2000 
times hotter than red hot iron. This temperature would 
be sufficient to volatilize the most obdurate substances, 
and to expand the vapor to vast dimensions ; and the op- 
posite effects of the extreme cold to which it would be 



293. Does the extreme tenuity of this body prevent its mov- 
ing in obedience to the laws that regulate the motions of the 
largest bodies in the system ? 

294. Is the physical nature of comets well understood ? How 
are the variations in the lengths of their tails accounted for ? 
How near did the comet of 1 680 approach to the sun ? What 
heat did it acquire ? Does this account for the direction of the 
tail ? How is that accounted for by some writers ? 



CEBITS AND MOTIONS OF C03IETS. 233 

subject in the regions remote from the sun, would be ad- 
equate to condense it into its former volume. 

This explanation, however, does not account for the 
direction of the tail, extending as it usually does, only 
in a line opposite to the sun. Some writers therefore, 
as Delambre, suppose that the nebulous matter of the 
comet after being expanded to such a volume, that the 
particles are no longer attracted to the nucleus unless by 
the slightest conceivable force, are carried off in a direc- 
tion from the sun, by the impulse of the solar rays them- 
selves. But to assign such a power of communicating 
motion to the sun's rays while they have never been 
proved to have any momentum, is unpliilosophical ; and 
we are compelled to place the phenomena of comets' 
tails among the points of astronomy yet to be explained. 

295. Since those comets which have their perihelion 
very near the sun, like the comet of 1680, cross the or- 
bits of all the planets, the possibility that one of them 
may strike the earth, has frequently been suggested. 
Still it may quiet our apprehensions on this subject, to 
reflect on the vast extent of the planetary spaces, in 
which these bodies are not crowded together as we see 
them erroneously represented in orreries and diagrams, 
but are sparsely scattered at immense distances from 
each other. They are lilie insects flying in the expanse 
of heaven. If a comet's tail lay with its axis in the 
plane of the ecliptic when it was near the sun, we can 
imagine that the tail might sweep over the earth ; but 
the tail may be situated at any angle with the ecliptic 
as well as in the same plane with it, and the chances 



295. What is said respecting the possibility of a comet's stri- 
king the earth? What considerations may quiet our apprehen- 
sions ? How might the case be if the tail lay in the plane of 
the ecliptic ? Is it probable that a comet will cross the ecliptic 
precisely at the place of the earth's path ? Have comets ac- 
tually approached near to the earth ? What would be the con- 
sequences were a comet to strike the earth ? 
20* 



284 COMETS. 

that it will not be in the same plane, are almost infinite. 
It is also extremely improbable that a comet will cross 
the plane of the ecliptic precisely at the earth's path in 
that plane, since it may as probably cross it at any other 
point, nearer or more remote from the sun. Still some 
comets have occasionally approached near to the earth. 
Thus Biela's comet in returning to the sun in 1832, 
crossed the ecliptic very near to the earth's track, and 
had the earth been then at that point of its orbit, it might 
have passed through a portion of the nebulous atmos- 
phere of the comet. The earth was within a month of 
reaching that point. This might at first view seem to 
involve some nazard ; yet we must consider that a 
month short, implied a distance of nearly 50,000,000 
miles. La Place has assigned the consequences that 
would ensue in case of a direct collision between the 
earth and a comet ; but terrible as he has represented 
them on the supposition that the nucleus of the comet 
is a solid body, yet considering a comet (as most of them 
doubtless are) as a mass of exceedingly light nebulous 
matter, it is not probable, even were the earth to make 
its way directly through a comet, that a particle of the 
comet would reach the earth. The portions encountered 
by the earth, would be arrested by the atmosphere, and 
probably inflamed ; and they would perhaps exhibit, on 
a more magnificent scale than was ever before observed, 
the phenomena of shooting stars, or meteoric showers. 



PART III. OF THE FIXED STARS AND THE SYS- 
TEM OF THE WORLD. 



CHAPTER I. 

OF THE FIXED STARS CONSTELLATIOXS. 

296. The Fixed Stars are so called, because, to 
common observation, they always maintain the same 
situations ^vith respect to one another. 

The stars are classed by their apparent magnitudes. 
The whole number of magnitudes recorded are sixteen, 
of which the first six only are visible to the naked eye ; 
the rest are telescopic stars. These magnitudes are not 
determined by any YQry definite scale, but are merely 
ranked according to their relative degrees of brightness, 
and this is left in a great measure to the decision of the 
eye alone. The brightest stars to the number of 15 or 
20, are considered as stars oi the first magnitude ; the 50 
or 60 next brightest, of the second magnitude ; the next 
200 of the third magnitude ; and thus the number of 
each class increases rapidly as we descend the scale, so 
that no less than fifteen or twenty thousand are included 
within the first seven magnitudes. 

297. The stars have been grouped in Constellations 
from the most remote antiquity ; a few, as Orion, Bootes, 
and Ursa Major, are mentioned in the most ancient wri- 
tings under the same names as they bear at present. 
The names of the constellations are sometimes founded 



296. Fixed Stars. — Why so called ? How classed 1 Into 
how many magnitudes are they divided ? How many are there 
of each magnitude ? 



236 FIXED STARS. 

on a supposed resemblance to the objects to which the 
names belong ; as the Swan and the Scorpion were evi- 
dently so denominated from their likeness to those ani- 
mals ; but in most cases it is impossible for us to find 
any reason for designating a constellation by the figure 
of the animal or the hero which is employed to repre- 
sent it. These representations were probably once 
blended with the fables of pagan mythology. The 
same figures, absurd as they appear, are still retained for 
the convenience of reference ; since it is easy to find 
any particular star, by specifying the part of the figure 
to which it belongs, as when we say a star is in the neck 
of Taurus, in the knee of Hercules, or in the tail of the 
Great Bear. This method furnishes a general clue to 
its position ; but the stars belonging to any constellation 
are distinguished according to their apparent magnitudes 
as follows : — first, by the Greek letters, Alpha, Beta, 
Gamma, &c. Thus Alpha Orionis, denotes the largest 
star in Orion ; Beta Andromedce, the second star in An- 
dromeda ; and Gamma Leonis, the third brightest star 
in the Lion. Where the number of the Greek letters is 
insufficient to include all the stars in a constellation, 
recourse is had to the letters of the Roman alphabet, a, 
b, c, &:c. ; and, in cases where these are exhausted, the 
final resort is to numbers. This is evidently necessary, 
since the largest constellations contain many hundrerds 
or even thousands of stars. Catalogues of particular 
stars have also been published by different astronomers, 
each author numbering the individual stars embraced in 
his Hst, according to the places they respectively occupy 
in the catalogue. These references to particular cata- 
logues are sometimes entered on large celestial globes. 
Thus we meet with a star marked 84 H., meaning that 



297. Constellations. — How long known ? Which are men- 
tioned in the most ancient writings ? How far are the names 
fomided on resemblance ? Why are the ancient figures still 
retained ? How are the individual stars of a constellation dis- 
tinguished ? What is said of catalogues of the stars ? 



FIXED STARS. 237 

this is its number in Herschel's catalogue ; or 140 M., de- 
noting the place the star occupies in the catalogue of 
Mayer. 

298. The earliest catalogue of the stars was made by 
Hipparchus of the Alexandrian school, about 140 years 
before the Christian era. A new star appearing in the 
firmament, he was induced to count the stars and to re- 
cord their positions, in order that posterity might be able 
to judge of the permanency of the constellations. His 
catalogue contains all that were conspicuous to the 
naked eye in the latitude of Alexandria, being 1022. 
Most persons unacquainted with the actual number of 
the stars which compose the visible firmament, would 
suppose it to be much greater than this ; but it is found 
that the catalogue of Hipparchus, embraces nearly all 
that can now be seen in the same latitude, and that on 
the equator, when the spectator has the northern and 
southern hemispheres both in view, the number of stars 
that can be counted does not exceed 3000. A careless 
view of the firmament in a clear night, gives us the im- 
pression of an infinite multitude of stars ; but when we 
begin to count them, they appear much more sparsely 
distributed than we supposed, and large portions of the 
sky appear almost destitute of stars. 

By the aid of the telescope, new fields of stars present 
themselves of boundless extent ; the number contin- 
ually augmenting as the powers of the telescope are in- 
creased. Lalande, in liis Histoire Celeste, has registered 
the positions of no less than 50,000 ; and the whole 
number visible in the largest telescopes amounts to many 
milhons. 

299. It is strongly recommended to the learner to ac- 
quaint himself vrith the leading constellations at least, 



298. Why did Hipparchus make a catalogue ? How many 
stars did he number ? What is the greatest number that can 
be seen by the naked eye in both hemispheres ? How many 
can be seen by the telescope ? 



238 FIXED STARS. 

and with a few of the most remarkable individual stars. 
The task of learning them is comparatively easy, and 
hardly any kind of knowledge, attained with so little 
labor, so amply rewards the possessor. It will generally 
be advisable, at the outset, to get some one already ac- 
quainted with the stars, to point out a few of the most 
conspicuous constellations, those of the Zodiac for ex- 
ample ; the learner may then resort to maps of the stars, 
or what is much better, to a celestial globe,* and fill up 
the outline by tracing out the principal stars in each 
constellation as there laid down. By adding one new 
constellation to his Hst every night, and reviewing those 
already acquired, he will soon become famihar with the 
stars, and will greatly augment his interest and improve 
his intelligence in celestial observations, and practical 
astronomy. 

CONSTELLATIONS. 

300. We will point out particular marks by which the 
leading constellations may be recognized, leaving it to 
the learner, after he has found a constellation, to trace 
out additional members of it by the aid of the celestial 
globe, or by maps of the stars. Let us begin with the 
Constellations of the Zodiac, which succeeding each 
other as they do in a known order, are most easily 
found. 

Aries (The Ram) is a small constellation, known by 
two bright stars which form his head. Alpha and Beta 
Arietis. These two stars are four degreesf apart, and 
directly south of Beta at the distance of one degree, is 



299. Specify the directions for learning the constellations. 



* For the method of rectifying the globe so as to represent the ap- 
pearance of the heavens on any particular evening, see page 34, Art. 
61. 

t These measures are not intended to be stated with exactness, but 
only with such a degree of accuracy as may serve for a general guide. 



CONSTELLATIONS. 239 

a smaller star, Gamma Arietis. It has been already 
intimated (Art. 139) that the vernal equinox probably 
was near the head of Aries, when the signs of the Zo- 
diac received their present names. 

Taurus (The Bull) will be readily found by the 
seven stars or Pleiades, which lie in his neck. The 
largest star in Taurus is Aldehara.n, in the Bull's eye, a 
star of the first magnitude, of a reddish color somewhat 
resembling the planet Mars. Aldebaran and four other 
stars in the face of Taurus, compose the Hyades. 

Gemini (The Twins) is known by two very bright 
stars. Castor and Pollux, four degrees asunder. Castor 
(the northern) is of the first, and Pollux of the second 
magnitude. 

Cancer (The Crab.) There are no large stars in this 
constellation, and it is regarded as less remarkable than 
any other in the Zodiac. It contains however an inter- 
esting group of small stars, called Prcesepe or the Neb- 
ula of Cancer, which resembles a comet, and is often 
mistaken for one, by persons unacquainted vnth the 
stars. With a telescope of very moderate powers this 
nebula is converted into a beautiful assemblage of ex- 
ceedingly bright stars. 

Leo (The Lion) is a very large constellation, and has 
many interesting members. Regulus {Alpha Leonis) 
is a star of the first magnitude, which lies directly in the 
ecliptic, and is much used in astronomical observations. 



300. Constellations of the Zodiac. — Aries. — How known ? 
How far are the two brightest stars apart ? Where was the 
vernal equinox situated when the signs of the Zodiac received 
their present names ? 

Taurus. — How found 1 Name the largest star in Taurus. 
What stars compose the Hyades ? 

Gemini. — How known ? How far are Castor and Pollux 
asunder ? Of what magnitudes are they respectively ? 

Cancer. — Are there any large stars in Cancer ? What is 
said of Praesepe ? 

Leo. — What is its size ? What is said of Regulus ? Where 
is the sickle ? Where is Denebola situated ? 



240 riXED STARS. 

North of Regulus lies a semi-circle of bright stars, form- 
ing a sickle of which Regulus is the handle. Denebola, 
a star of the second magnitude, is in the Lion's tail, 25° 
north east of Regulus. 

Virgo (The Virgin) extends a considerable way 
from west to east, but contains only a few bright stars. 
Spica, however, is a star of the first magnitude, and 
lies a little east of the place of the autumnal equinox. 
Twenty-two degrees north of Spica, is Vindemiatrix, in 
the arm of Virgo, a star of the third magnitude. 

Libra (The Balance) is distinguished by three large 
stars, of which the two brightest constitute the beam 
of the balance, and the smallest forms the top or handle. 

Scorpio (The Scorpion) is one of the finest of the 
constellations. His head is formed of five bright stars 
arranged in the arc of a circle, which is crossed in the 
center by the ecliptic nearly at right angles, near the 
brightest of the five. Beta Scorjnonis. Nine degrees 
southeast of this, is a remarkable star of the first mag- 
nitude, of a reddish color, called Co?^ Scorpionis, or An- 
tares. South of this a succession of bright stars sweep 
round towards the east, terminating in several small 
stars, forming the tail of the Scorpion. 

Sagittarius (The Archer.) Northeast of the tail of 
the Scorpion, are three stars in the arc of a circle which 
constitute the bow of the Archer, the central star being 
the brightest, directly west of which is a bright star 
which forms the arrow. 

Capricornus (The Goat) lies northeast of Sagittarius, 
and is known by two bright stars, three degrees apart, 
which form the head. 



Virgo. — Extent from east to west ? What is said of Spica, 
and of Vindemiatrix ? 

Libra. — How distin^ished ? 

Scorpio. — His appearance ? His head how formed ? Where 
is Antares situated ? 

Sagittarius. — Describe his bow. 

Capricornus. — Where situated from Sagittarius ? How 
known ? 



CONSTELLATIONS. 241 

Aquarius (The Water Bearer) is recognized by- 
two stars in a line with Alpha Capricorni, forming the 
shoulders of the figure. These two stars are 10^ apart, 
and 4° southeast is a third star, which, together with the 
other two, makes an acute triangle, of which the west- 
ernmost is the vertex, 

Pisces (The Fishes) lie between Aquarius and Aries. 
They are not distinguished by any large stars, but are 
connected by a series of small stars, that form a crooked 
line between them, Piscis Australis, the Southern 
Fish, lies directly below Aquarius, and is known by a 
single bright star far in the south, having a dechnation 
of 30°. The name of this star is Fomalhaitt, and it is 
much used in astronomical measurements. 

301. The Constellations of the Zodiac, being first 
well learned, so as to be easily recognized, will facil- 
itate the learning of others that lie north and south of 
them. Let us therefore next review the principal North- 
ern Constellations, beginning north of Aries and pro- 
ceeding from west to east 

Androsieda, is characterized by three stars of the sec- 
ond magnitude, situated in a straight line, extending 
from west to east. The middle star is about 17° north 
of Beta Arietis. It is in the girdle of Andromeda, and 
is named Mirach, The other two He at about equal 
distances, 14° west and east of Mirach. The western 
star, in the head of Andromeda, lies in the Equinoctial 
Colure. The eastern star, Alamak, is situated in the 
foot- 

Perseus lies directly north of the Pleiades, and con- 
tains several bright stars. About 18° from the Pleiades 



Aquarius. — How recognized 1 How far apart are the shoul- 
ders of Aquarius ? 

Pisces. — Where situated 1 How connected ? Where is 
Piscis Australis situated 1 By what name is it commonly 
known ? 

301. Northern Constellations. AncfrwTzec^a, how character- 
ized ? Where are Mirach and Alamak situated ? 
21 



242 FIXED STARS. 

is Algol, a star of the second magnitude in the Head of 
Medusa, which forms a part of the figure ; and 9° north- 
east of Algol is Algenih, of the same magnitude in the 
back of Perseus. Between Algenib and the Pleiades are 
three bright stars, at nearly equal intervals, which com- 
pose the right leg of Perseus. 

Auriga (the Wagoner) lies directly east of Perseus, 
and extends nearly parallel to that constellation from 
north to south. Capella a very white and beautiful 
star of the first magnitude, distinguishes this constella- 
tion. The feet of Auriga are near the Bull's Horns. 

The Lynx comes next, but presents nothing particu- 
larly interesting, containing no stars above the fourth 
magnitude. 

Leo Minor consists of a collection of small stars 
north of the sickle in Leo, and south of the Great Bear. 
Its largest star is only of the third magnitude. 

Coma Berenices is a cluster of small stars, north of 
Denebola, (a star in the tail of the Lion,) and of the head of 
Virgo. About 12° north of Berenice's Hair, is a single 
bright star called Cor Caroli, or Charles's Heart. 

Bootes, which comes next, is easily found by means 
of Arcturus, a star of the first magnitude, of a reddish 
color, which is situated near the knee of the figure. 
Arcturus is accompanied by three small stars forming a 
triangle a little to the southwest. Two bright stars 
Gamma and Delta Bootis, form the shoulders, and 
Beta of the third magnitude is in the head of the 
figure. 

Corona Borealis, (The Crown,) which is situated east 



Perseus. — How situated with respect to the Pleiades ? 
Where is Algol ? Where is Algenib ? What stars compose 
the right leg of Perseus ? 

Auriga.— How situated from Perseus ? What large star dis- 
tinguishes this constellation ? Where are the feet of Auriga ? 

Lynx. — Size of its stars ? 

Leo Minor. — Where situated ? Size of its largest star 1 

Coma Berenices. — Describe it. Where is Cor CaroU ? 

Bootes. — What large star is in this constellation ? 



COJfSTELLATIONS. 243 

of Bootes, is very easily recognized, composed as it is of 
a semi-circle of bright stars. In the center of the bright 
crown, is a star of the second magnitude, called Gem- 
ma ; the remaining stars are all much smaller. 

Hercules, lying between the Crown on the west and 
the Lyre on the east, is very thick set with stars, most 
of which are quite small. The Constellation covers a 
great extent of the sky, especially from N. to S., the 
head terminating ^vithin 15° of the equator, and marked 
by a star of the third magnitude, called Has Algethiy 
which is the largest in the Constellation. 

Ophiucus is situated directly south of Hercules, ex- 
tending some distance on both sides of the equator, the 
feet resting on the Scorpion. The head terminates near 
the head of Hercules, and like that, is marked by a 
bright star witliin 5° of Alpha Herciilis. Ophiucus is 
represented as holding in his hands the Serpent, the 
head of which, consisting of three bright stars, is sit- 
uated a little south of the Crov/n. The folds of the 
serpent will be easily followed by a succession of bright 
stars which extend a great way to the east. 

Aquila (The Eagle) is conspicuous for three bright 
stars in its neck, of which the central one, Altair, is a 
very brilhant white star of the first magnitude. Anti- 
nous lies directly south of the Eagle, and north of the 
head of Capricornus. 

Delphinus (The Dolphin) is a small but beautiful 
Constellation, a few degrees east of the Eagle, and is 
characterized by four bright stars near to one another, 
forming a small rhombic square. Another star of the 
same mao^nitude 5*^ south, makes the tail. 



Corona Borealis. — Describe it. Where is Gemma situated ? 

Hercules. — Between what two constellations is it ? What 
is said of its extent ? Where is Ras Algethi ? 

Ophiucus. — Where is it from Hercules ? How is it repre- 
sented ? 

Aquila. — How distniguished ? Where is Altair ? Where is 
Antinous 1 

The Dolphin. — Describe it. 



244 FIXED STARS. 

Pegasus lies between Aquarius on the southwest and 
Andromeda on the northeast. It contains but few large 
stars. A very regular square of bright stars is composed 
of Alpha AndrojiiedcB, and the three largest stars in Pe- 
gasus, namely, Scheat, Markab, and Algenih. The 
sides composing this square are each about 15^. Alge- 
nib is situated in the Equinoctial Colure. 

302. We may now review the Constellations which 
surround the North Pole, within the circle of perpetual 
apparition. (Art. 38.) 

Ursa Minor (The Little Bear) lies nearest the 
pole. The Pole-star, Polaris, is in the extremity of the 
tail, and is of the third magnitude. Three stars in a 
straight line 4^^ or 5*^ apart, commencing with the Pole- 
star, lead to a trapezium of four stars, and the whole 
seven form together a dipper, the trapezium being the 
body, and the three stars the handle. 

Ursa Major (The Great Bear) is situated between 
the pole and the Lesser Lion, and is usually recognized 
by the figure of a larger and more perfect dipper, which 
constitutes the hinder part of the animal. This has also 
seven stars, four in the body of the dipper, and three in 
the handle. All these are stars of much celebrit)/ The 
two in the western side of the dipper, Alpha and Beta, are 
called Pointers, on account of their always being in a 
right line with the Pole-star, and therefore affording an 
easy mode of finding that. The first star in the tail, next 
the body, is named Alioth, and the second Mizar. The 
head of the Great Bear lies far to the westward of the 



Pegasus. — Belween what two constellations is it situated ? 
How may a square be formed of certain stars in this constel- 
lation ? 

302. Northern Constellations. Ursa Minor. — How situated 
with respect to the pole ? Show how the dipper in this con- 
stellation is formed ? 

Ursa Major. — Where situated ? How recognized ? What 
are the Pointers ? Where is Alioth — Mizar ? Of what is the 
head composed ? 



CONSTELLATIONS. 245 

Pointers, and is composed of numerous small stars ; and 
the feet are severally composed of two small stars very 
near to each other. 

Draco (The Dragon) winds round between the Great 
and the Little Bear ; and commencing with the tail, be- 
tween the Pointers and the Pole-star, it is easily traced 
by a succession of bright stars extending from west to 
east, passing under Ursa Minor, it returns westward, and 
terminates in a triangle which forms the head of Draco, 
near the feet of Hercules, northwest of LryrsL. 

Cepheus lies eastward of the breast of the Dragon, 
but has no stars above the third magnitude. 

Cassiopeia is known by the figure of a chah\ com- 
posed of four stars which form the legs, and two which 
form the back. This constellation lies between Perseus 
and Cepheus, in the Milky Way. 

Cygnus (The Swan) is situated also in the Milky Way, 
some distance southwest of Cassiopeia, towards the Ea- 
gle. Three bright stars, which lie along the Milky 
Way, form the body and neck of the Swan, and two 
others in a line ^^dth the middle one of the three, one 
above and one below, constitute the wrings. This Con- 
stellation is among the few, that exhibit some resem- 
blance to the animals whose names they bear. 

I^YRA (The Lyre) is directly west of the Swan, and 
is easily distinguished by a beautiful white star of the 
first magnitude, Alpha Lyrce. 

303. The Southern Constellations are comparatively 
few in number. We shall notice only the Whale, Orion, 
the Greater and Lesser Dog, Hydra, and the Crow. 



Draco. — How situated with respect to the two Bears 1 
Trace its course ? 

Gepheus. — How situated from Draco ? 

Cassiopeia. — How known ? Where situated ? 

Cygnus. — How situated ? Of what stars formed ? Has this 
constellation any resemblance to a Swan 1 

303. Southern Constellations. Cetus. — Its extent ? Size 
of its stars 1 What is said of Menkar, and of Mira ? 
21* 



246 FIXED STARS. 

Cetus (The Whale) is distinguished rather for its 
extent than its brilliancy, reaching as it does through 
40° of longitude, while none of its stars except one, 
are above the third magnitude. Menkar {Alpha Ceti) 
in the mouth, is a star of the second magnitude, and 
several other bright stars directly south of Aries, make 
the head and neck of the Whale. Mira {Omicron 
Ceti) in the neck of the Whale is a variable star. 

Orion is one of the largest and most beautiful of the 
constellations, lying southeast of Taurus. A cluster of 
small stars form the head ; two large stars, Betalgeus of 
the first and Bellatrix of the second magnitude, make 
the shoulders ; three more bright stars compose the 
buckler, and three the sword ; and Rigel, another star of 
the first magnitude, makes one of the feet. In this 
Constellation there are 70 stars plainly visible to the 
naked eye, including two of the first magnitude, four of 
the second, and three of the third. 

Canis Major lies S. E. of Orion, and is distinguished 
chiefly by its containing the largest of the fixed stars, 
Sirius. 

Canis Minor a little north of the equator, between 
Canis Major and Gemini, is a small Constellation, con- 
sisting chiefly of two stars, of which Procyon is of the 
first magnitude. 

Hydra has its head near Procyon, consisting of a 
number of stars of ordinary brightness. About 17° S. 
E. of the head, is a star of the second magnitude, form- 
ing the heart, {Cor Hydi^ce ;) and eastward of this, is 
a long succession of stars of the fourth and fifth magni- 
tudes composing the body and the tail, and reaching a 
few degrees south of Spica Virginis. 

Orion. — What is said of its size and beauty ? Describe its 
different parts. How many stars does it contain which are 
visible to the naked eye ? 

Canis Major. — Where situated from Orion ? What large 
star is in it ? 

Canis Minor. — Where situated ? What large star does it 
contain ? 

Hydra. — Trace its course. 



CLUSTERS OF STARS. 247 

CoRvus (The Crow) is represented as standing on the 
tail of Hydra. It consists of small stars, onlv three of 
which are as large as the third magnitude. 

304. The foregoing brief sketch is designed merely 
to aid the student in finding the principal constellations 
and the largest fixed stars. When we have once learned 
to recognize a constellation by some characteristic marks, 
we may afterwards fill~up the outhne by the aid of a 
celestial globe or a map of the stars. It will be of little 
avail however, merely to commit this sketch to memory ; 
but it will be very useful for the student at once to ren- 
der himself famihar wdth it, from the actual specimens 
which every clear evening presents to his view. 



CHAPTER II. 



OF CLUSTERS OF STARS NEBULJE VARIABLE STARS 

TFSIPORARY STARS DOUBLE STARS. 

305. In various parts of the firmament are seen large 
groups or clusters, which, either by the naked eye, or by 
the aid of the smallest telescope, are perceived to con- 
sist of a great number of small stars. Such are the 
Pleiades, Coma Berenices, and Prsesepe or the Bee-hive 
in Cancer. The Pleiades, or Seven stars, as they are 
called, in the neck of Taurus, is the most conspicuous 
cluster. When we look directly at this group, we can- 
not distinguish more than six stars, but by turning the 
eye sideways* upon it, we discover that there are many 



Corvus, — How represented 1 

305. Clusters. — Name a few of the largest. Pleiades, 
where situated 1 How many stars does it contain ? What 
is said of Coma Berenices, and of the Bee-hive ? 

* Indirect vision is far more delicate than direct. Thus we can see 
the Zodiacal Light or a Comet's Tail, much more distinctly and better 
defined, if we fix one eye on a part of the heavens at some distance, and 
turn the other eye obliquely upon the object. 



248 FIXED STARS. 

more. Telescopes show 50 or 60 stars crowded to- 
gether and apparently insulated from the other parts of 
the heavens. Coma Berenices has fewer stars, but they 
are of a larger class than those which compose the Plei- 
ades. The Bee-hive or Nebula of Cancer as it is called, 
is one of the finest objects of tliis kind for a small tel- 
escope, being by its aid converted into a rich congeries 
of shining points. The head of Orion aftbrds an exam- 
ple of another cluster, though less remarkable than the 
others. 

306. NehulcB are those faint misty appearances which 
resemble comets, or a small speck of fog. The Galaxy 
or Milky Way, presents a continued succession of large 
nebulae. A very remarkable Nebula, visible to the naked 
eye, is seen in the girdle of Andromeda. No powers of 
the telescope have been able to resolve this into separate 
stars. Its dimensions are astonishingly great. In diam- 
eter it is about 15^. The telescope reveals to us innumer- 
able objects of this kind. Sir Wilham Herschel has given 
catalogues of 2000 Nebulse, and has shown that the neb- 
ulous matter is distributed through the immensity of 
space in quantities inconveivably great, and in separate 
parcels of all shapes and sizes, and of all degrees of 
brightness between a mere milky appearance and the 
condensed light of a fixed star. Finding that the gra- 
dations between the two extremes were tolerably regu- 
lar, he thought it probable that the nebulae form the ma- 
terials out of which nature elaborates suns and systems ; 
and he conceived that, in virtue of a central gravitation, 
each parcel of nebulous matter becomes more and more 
condensed, and assumes a rounded form. He inferred 
from the eccentricity of its shape, and the effects of the 
mutual gravitation of its particles, that it acquires gradu- 



306. Nc?j>ul(2. — What are they ? What is said of the nebula 
in the girdle of Andromeda? How many nebuire has Sir W. 
Herschel included in his catalogue ? What are his ideas re- 
specting nebulae ? 



NEBULJE. 249 

ally a rotary motion ; that the condensation goes on in- 
creasing until the mass acquires consistency and solidity, 
and all the characters of a comet or a planet ; that by a 
still further process of condensation, the body becomes a 
real star, self-sliining ; and that thus the waste of the ce- 
lestial bodies, by the perpetual diffusion of their light, is 
continually compensated and restored by new formations 
of such bodies, to replenish forever the universe with 
planets and stars. 

307. These opinions are recited here rather out of re- 
spect to their notoriety and celebrity, than because we 
suppose them to be founded on any better evidence than 
conjecture. The Philosophical Transactions for many 
years, both before and after the commencement of the 
present centuiy, abound w^th both the observations and 
speculations of Sir William Herschel. The former are 
deserving of all praise ; the latter of much less confi- 
dence. Changes, how^ever, are going on in some of the 
nebula3, which plainly show that they are not, hke plan- 
ets and stars, fixed and permanent creations. Thus the 
great nebula in the girdle of Andromeda, has very much 
altered its structure since it first became an object of tele- 
scopic observation. Many of the nebulae are of a globu- 
lar form, (Fig. 50,) but frequently they present the ap- 
pearance of a rapid increase of numbers towards the cen- 
(Fig. 50.) (Fig. 51.) 



ter, (Fig. 51,) the anterior boundary being irregular, 
and the central parts more nearly spherical. 



307. What is said of Herschel's speculations and of his ob- 
servations ] What changes occur in the nebulae ? What 
forms have they ? 



250 FIXED STARS. 

308. The nebula in the sword of Orion is particularly 
celebrated, being very large and of a peculiarly interest- 
ing appearance. According to Sir John Herschel, its 
nebulous character is very different from what might be 
supposed to arise from the assemblage of an immense 
collection of small stars. It is formed of little flocculent 
masses like ^visps of clouds ; and such wisps seem to 
adhere to many small stars at its outskirts, and especially 
to one considerable star which it envelops with a neb- 
ulous atmosphere of considerable extent and singular 
figure. 

Descriptions, however, can convey but a very imper- 
fect idea of this wonderful class of astronomical objects, 
and we would therefore urge the learner studiously to 
avail himself of the first opportunity he may have to 
view them through a large telescope, especially the Neb- 
ula of Andromeda and of Orion. 

309. Nebulous Stars are such as exhibit a sharp and 
brilliant star surrounded by a disk or atmosphere of neb- 
ulous matter. These atmospheres in some cases present 
a circular, in others an oval figure ; and in some in- 
stances, the nebula consists of a long, narrow spindle- 
shaped ray, tapering away at both ends to points. 

Planetary Nehulce constitute another variety, and are 
very remarkable objects. They have, as their name 
imports, exactly the appearance of planets. Whatever 
may be their nature, they must be of enormous magni- 
tude. One of them is to be found in the parallel of 
Gamma Aquarii, and about 5m. preceding that star. Its 
apparent diameter is about 20"'. Another in the Con- 
stellation Andromeda, presents a visible disk of \2'\ per- 
fectly defined and round. Granting these objects to be 



308. What is said of the nebula in the sword of Orion ? 
Can the nebulae be fully learned from description ? 

309. Nebulous stars — what are they? What forms ha^e 
their atmospheres ? Planetary nebulaj, — their appearance ? 
What apparent diameters have they ? What is said of their 
Hght ? 



VARIABLE STARS. 251 

equally distant from us with the stars, their real dimen- 
sions must be such as, on the lowest computation, would 
fill the orbit of Uranus. It is no less evident that, if they 
be solid bodies, of a solar nature, the intrinsic splendor 
of their surfaces must be almost infinitely inferior to 
that of the sun. A circular portion of the sun's disk, 
subtending an angle of 20^^, would give a light equal to 
100 full moons ; while the objects in question are hardly, 
if at all, discernible with the naked eye. 

310. The Galaxy or Milky Way is itself supposed 
by some to be a nebula of which the sun forms a com- 
ponent part ; and hence it appears so much greater than 
other nebulae only in consequence of our situation ^vith 
respect to it, and its greater proximity to our system. 
So crowded are the stars in some parts of this zone, that 
Sir WiUiam Herschel, by counting the stars in a single 
field of his telescope, estimated that 50,000 had passed 
under his review in a zone two degrees in breadth du- 
ring a single hour's observation. Notwithstanding the 
apparent contiguity of the stars which crowd the galaxy, 
it is certain that their mutual distances must be incon- 
ceivably great. 

311. Variable Stars are those which undergo a pe- 
riodical change of brightness. One of the most remark- 
able is the star Mira in the Whale, {Omicron Ceti.) It 
appears once in 1 1 months, remains at its greatest bright- 
ness about a fortnight, being then, on some occasions, 
equal to a star of the second magnitude. It then de- 
creases about three months, until it becomes completely 
invisible, and remains so about five months, when it 
again becomes visible, and continues increasing during 
the remaining three months of its period. 

Another very remarkable variable star is Algol (Beta 
Persei.) It is usually visible as a star of the second magni- 



310. Galaxy or Milky Way — what is said respecting it ? 
Give an example of the multitude of stars in it ? 



252 FIXED STAES. 

tude, and continues such for 2d. 14h. when it suddenly 
begins to diminish in splendor, and in about 3^ hours is 
reduced to the fourth magnitude. It then begins again 
to increase, and in 3^ hours more, is restored to its usual 
brightness, going through all its changes in less than 
three days. This remarkable law of variation appears 
sti'ongly to suggest the revolution round it of some opake 
body, which, when interposed between us and Algol, 
cuts off a large portion of its light. It is (says Sir J. 
Herschel) an indication of a high degree of activity in 
regions where, but for such evidences, we might con- 
clude all lifeless. Our sun requires almost nine times 
this period to perform a revolution on its axis. On the 
other hand, the periodic time of an opake revolving 
body, sufficiently large, which would produce a similar 
temporary obscuration of the sun, seen from a fixed star, 
would be less than fourteen hours. 

The duration of these periods is extremely various. 
While that of Beta Persei above mentioned, is less than 
three days, others are more than a year, and others many 
years. 

312. Temporary Stars are new stars which have ap- 
peared suddenly in the firmament, and after a certain in- 
terval, as suddenly disappeared and returned no more. 

It was the appearance of a new star of this kind 125 
years before the Christian era, that prompted Hipparchus 
to draw up a catalogue of the stars, the first on record. 
Such also was the star which suddenly shone out A. D 
389, in the Eagle, as bright as Venus, and after remain- 
ing three weeks disappeared entirely. At other periods, 
at distant intervals, similar phenomena have presented 
themselves. Thus the appearance of a star in 1572, 
was so sudden, that Tycho Brahe returning home one 



311. Variable stars — what are they ? What is said of Mira ? 
Also of Algol ? How are their periods of revolution ? 

312. Temporary stars — what are they ? Give examples. 
Do they ever return ? Do stars ever disappear ^ 



DOUBLE STARS. 253 

day was surprized to find a collection of country people 
gazing at a star which he was sure did not exist half an 
hour before. It was then as bright as Sirius, and con- 
tinued to increase until it surpassed Jupiter when bright- 
est, and was visible at mid-day. In a month it began 
to diminish, and in three months afterwards it had en- 
tirely disappeared. 

It has been supposed by some that in a few instances, 
the same star has returned, constituting one of the peri- 
odical or variable stars of a long period. 

Moreover, on a careful re-examination of the heavens, 
and a comparison of catalogues, many stars are now 
found to be missing. 

313. Double vStars are those which appear single to 
the naked eye, but are resolved into two by the tele- 
scope ; or, if not visible to the naked eye, are seen in the 
telescope so close together as to be recognized as objects 
of this class. Sometimes three or more stars are found 
in this near connexion, constituting triple or multiple 
stars. Castor, for example, when seen by the naked 
eye, appears as a single star, but in a telescope even of 
moderate powers, it is resolved into two stars of between 
the third and fourth magnitudes, within 5^^ of each other. 
These two stars are nearly of equal size, but frequently 
one is exceedingly small in comparison with the other, 
resembling a satellite near its primary, although in dis- 
tance, in light, and in other characteristics, each has all 
the attributes of a star, and the combination therefore 
cannot be that of a planet with a satelhte. In some in- 
stances, also, the distance between these objects is much 
less than 5^^, and in many cases it is less than V\ The 
extreme closeness, together w^ith the exceeding minute- 
ness of most of the double stars, requires the best tele- 



313. Double stars — what are they? What are multiple 
stars ? Give an example of a double star ? How do the two 
stars sometimes differ ? What is required in order to observe 
most of the double stars ? 

22 



254 



FIXED STARS. 



scopes united with the most acute powers of observa- 
tion. Indeed, certain of these objects are regarded as 
the severest tests, both of the excellence of the instru- 
ment and of the skill of the observer. The following 
diagram represents four double stars, as seen with ap- 
propriate magnifiers. No. 1. exhibits Epsilon Bootis with 
a power of 350 ; No. 2, Rigel with a power of 130 ; 
No. 3, the Pole-star with a power of 100 ; and No. 4, 
Castor with a power of 300. 

Fig. 52. 
12 3 4 




314. Our knowledge of the double stars almost com- 
menced w^ith Sir William Herschel, about the year 1780. 
At the time he began his search for them, he was ac- 
quainted with or\\y four. Within five years, he discov- 
ered nearly 700 double stars.* In his memoirs, pub- 
lished in the Philosophical Transactions, he gave most 
accurate measurements of the distances between the two 
stars, and of the angle which a line joining the two, 
formed with the parallel of declination. These data 
would enable him, or at least posterity, to judge whether 
these minute bodies ever change theu' position with re- 
spect to each other. 



314. Who began the discovery of double stars ? When did 
he publish his account of them ? By whom have these re- 
searches been since prosecuted ? What two circumstances add 
a high degree of interest to the phenomena of the double stars ? 



* During his life he observe^ in all, 2400 double stars. 



MOTIONS OF THE FIXED STARS. 255 

Since 1821, these researches have been prosecuted 
with great zeal and industiy by Sir James South and 
Sir John Herschel in England, and by Professor Struve 
at Dorpat in Russia ; and the whole number of double 
stars now known, amounts to several thousands. Two 
circumstances add a high degree of interest to the phe- 
nomena of the double stars — the first is, that a few of 
them at least are found to have a revolution around 
each other, and the second, that they are supposed to 
afford the means of obtaining the parallax of the fixed 
stars. Of these topics we shall treat in the next chapter. 



CHAPTER III. 

OF THE MOTIONS OF THE FIXED STARS DIST^\JfCES— 

NATURE. 

315. In 1803, Sir William Herschel first determined 
and announced to the world, that there exist among the 
stars, separate systems, composed of tw^o stars revolving 
about each other in regular orbits. These he denomin- 
ated Binary Stars, to distinguish them from other 
double stars w^here no such motion is detected, and 
whose proximity to each other may possibly arise from 
casual juxta-position, or from one being in the range of 
the other. Between fifty and sixty instances of changes 
to a greater or less amount of the relative position of 
double stars, are mentioned by Sir William Herschel ; 
and a few of them had changed their places so much 
v/ithin 25 years, and in such order, as to lead him to the 
conclusion that they performed revolutions, one around 
the other, in regular orbits. 



315. Binary Stars. — Who first discovered this class of 
bodies 1 How are they distinguished from ordinary double 
stars 1 What conclusions did Sir W. Herschel draw respect- 
ing them ? 



256 



FIXED STARS. 



316. These conclusions have been fully confirmed by 
later observers, so that it is now considered as fully es- 
tablished, that there exist among the fixed stars, binary 
systems, in which two stars perform to each other the 
office of sun and planet, and that the periods of revolu- 
tion of more than one such pair have been ascertained 
with something approaching to exactness. Immersions 
and emersions of stars behind each other have been ob- 
served, and real motions among them detected rapid 
enough to become sensible and measurable in very short 
intervals of time. The following table exhibits the 
present state of our knowledge on this subject.* 



Names. 


Period in years. 


Major axis of the orbit. 


Ecceutricity. 


'^Coronas, 
CCancri, 
lUrsse Majoris, 
70 Ophiuchi 
Castor, 
aCoronae, 
61 Cygni, 
/Virginis, 
/Leonis, 


43.40 

55.00 

58.26 

80.34 

252.66 

286.00 

452.00 

628.90 

1200.00 










7^^714 
8.784 

16.172 
7.358 

30.860 

24.000 


0.4164 
0.4667 
0.7582 
0.6112 


0.8335 







From this table it appears, first, that the periods of the 
double stars are very various, ranging, in the case of 
those already ascertained, from forty-three years to one 



316. Have the conclusions of Herschel been confirmed t)y 
others ? What doctrine is now considered as fully established ? 
How are the periods of the double stars ? What is the figure of 
their orbits ? Which is the most remarkable of the Binary 
stars ? What is its size ? How long since it was first observed 
to be double ? What changes has it undergone since ? When 
did it pass its perihelion ? 



* Those who do not understand the Greek letters, can pass over this 
table to the inferences which follow. 



MOTIONS OP THE FIXED STARS. 257 

thousand ; secondly, that thoir orbits are very small 
ellipses, more eccentric than those of the planets, the 
greatest of which (that of Mercury) having an eccentri- 
city of only about .2 of the major axis. 

The most remarkable of the binary stars is Gamma 
Virginis, on account not only of the length of its period, 
but also of the great diminution of apparent distance, 
and rapid increase of angular motion about each other 
of the individuals composing it. It is a bright star of 
the fourth magnitude, and its component stars are almost 
exactly equal. It has been known to consist of two 
stars since the beginning of the eighteenth century, their 
distance being then between six and seven seconds ; so 
that any tolerably good telescope would resolve it. 
Since that time they have been constantly approaching, 
and are at present hardly more than a single second asun- 
der ; so that no telescope that is not of a very superior 
quality, is competent to show them otherwise than as a 
single star, somewhat lengthened in one direction. It 
fortunately happens that Bradley (Astronomer Royal) in 
1718, noticed, and recorded in the margin of one of his 
observation books, the apparent direction of their line of 
junction, as being parallel to that of two remarkable 
stars Alpha and Delta of the same constellation, as seen 
by the naked eye, — a remark which has been of signal 
service in the investigation of their orbit. It is found 
that it passed its perihelion, August 18th, 1834. 

317. The revolutions of the binary stars have assured 
us of that most interesting fact, that the law of gravita- 
tion extends to the fixed stars. Before these discoveries, 
we could not decide except by a feeble analogy that this 
law transcended the bounds of the solar system. In- 



17. What great fact have the revolutions of the binary stars 
revealed to us ? How was this doctrine limited before this 
discovery 1 Are these revolutions those of a planetary or 
cometary nature ? 

22* 



258 FIXED STARS. 

deed, our belief of the fact rested more upon our idea of 
unity of design in all the works of the Creator, than 
upon any certain proof; but the revolution of one star 
around another in obedience to forces which must be 
similar to those that govern the solar system, establishes 
the grand conclusion, that the law of gravitation is truly 
the law of the material universe. 

We have the same evidence (says Sir John Herschel) 
of the revolutions of the binary stars about each other, 
that we have of those of Saturn and Uranus about the 
sun ; and the correspondence between their calculated 
and observed places in such elongated ellipses, must be 
admitted to carry with it a proof of the prevalence of the 
Newtonian law of gravity in their systems, of the very 
same nature and cogency as that of the calculated and 
observed places of comets round the center of our own 
system. 

But (he adds) it is not with the revolution of bodies 
of a planetary or cometary nature round a solar center 
that we are now concerned ; it is with that of sun 
around sun, each, perhaps, accompanied with its train of 
planets and their satellites, closely shrouded from our 
view by the splendor of their respective suns, and crowd- 
ed into a space, bearing hardly a greater proportion to 
the enormous interval which separates them, than the 
distances of the satellites of our planets from their pri- 
maries, bear to their distances from the sun itself. 

318. Some of the fixed stars appear to have a real mo- 
tion in space. 

There are several apparent changes of place among 
the stars which arise from real changes in the earth, 
which, as we are not conscious of them, we refer to the 
stars ; but there are other motions among the stars which 



318. Have any of the fixed stars a real motion in space ? 
Are the places of the stars as described in ancient times by 
Ptolemy nearly the same as at present ? To what conclu- 
sions on this subject are we now forced ? 



MOTIONS OP THE FIXED STARS. 259 

cannot result from any changes in the earth, but must 
arise from changes in the stars themselves. Such mo- 
tions are called the proper motions of the -stars. Nearly 
2000 years ago, Hipparchus and Ptolemy made the most 
accurate determinations in their power of the relative 
situations of the stars, and their observations have been 
transmitted to us in Ptolemy's Almagest ; from which it 
appears that the stars retain at least very nearly the same 
places now as they did at that period. Still the more 
accurate methods of modern Astronomers, have brought 
to light minute changes in the places of certain stars, 
which force upon us the conclusion, either that our solar 
system causes an apparent displacement of certain stars, 
hy a motion of its own in space, or that they have them- 
selves a proper motion. Possibly, indeed, both these 
causes may operate. 

319. If the sun, and of course the earth which accom- 
panies him, is actually in motion, the fact may become 
manifest from the apparent approach of the stars in the 
region which he is leaving, and the recession of those 
which lie in the part of the heavens towards which he 
is travelling. Were two groves of trees situated on a 
plain at some distance apart, and we should go from one 
to the other, the trees before us would gradually appear 
farther and farther asunder, while those we left behind 
would appear to approach each other. Some years since. 
Sir WilHam Herschel supposed he had detected changes 
of this kind among two sets of stars in opposite points 
of the heavens, and announced that the solar system 
was in motion towards a point in the constellation Her- 
cules ; but other astronomers have not found the changes 
in question such as would correspond to this motion, or 



319. If the solar system is really in motion, how may the 
fact become manifest ? Towards what constellation did Sir 
WiUiam Herschel suppose it moving ? Has the opinion been 
confirmed by later observers 1 



260 FIXED STARS. 

to any motion of the sun ; and while it is a matter of 
general belief that the sun has a motion in space, the 
fact is not considered as yet entirely proved. 

320. In most cases where a proper motion in certain 
stars has been suspected, its annual amount has been so 
small, that many years are required to assure us, that the 
effect is not owing to some other cause than a real pro- 
gressive motion in the stars themselves ; but in a few 
instances the fact is too obvious to admit of any doubt. 
Thus the two stars 61 Cygni, which are nearly equal, 
have remained constantly at the same, or nearly at the 
same distance of 15^^ for at least fifty years past. Mean- 
while they have shifted their local situation in the 
heavens, 4' 23^^ the annual proper motion of each star 
being 5^''. 3, by which quantity this system is every year 
carried along in some unknown path, by a motion which 
for many centuries must be regarded as uniform and rec- 
tillinear. A greater proportion of the double stars than 
of any other indicate proper motions, especially the bi- 
nary stars or those which have a revolution around each 
other. Among stars not double, and no way differing 
from the rest in any other obvious particular, Mu Cassi- 
oj^eicB has the greatest proper motion of any yet ascer- 
tained, amounting to nearly 4'^ annually. 

DISTANCES OF THE FIXED STARS. 

321. We cannot ascertain the actual distance of any 
of the fixed stars, hut can certainly determine that the 
nearest star is more than (20,000,000,000,000,) twenty 
billions of miles from the earth. 



320. What length of time is required in order to detect 
proper motions in the stars ? What changes have occurred in 
the two stars 61 Cygni? What sort of stars indicate proper 
motions ? Of stars not double, what star has the greatest 
proper motion ? 



DISTANCES OF THE PiXED STARS. 261 

For all the measurements relating to the distances of 
the sun and planets, the radius of the earth furnishes the 
base line. (Art. 96.) The length of tliis hne being 
known, and the horizontal parallax of the body, whose 
distance is sought, we readily obtain the distance by tne 
solution of a right angled triangle. But any star viewed 
from the opposite sides of the earth, would appear from 
both stations, to occupy precisely the same situation in 
the celestial sphere, and of course it would exhibit no 
horizontal parallax. 

But astronomers have endeavored to find a parallax in 
some of the fixed stars, by taking the diameter of the 
earthbs orbit as a base line. Yet even a change of posi- 
tion amounting to 190 millions of miles, proves insuffi- 
cient to alter the place of a single star, from which it is 
concluded that the stars have not even any annual par- 
allax ; that is, the angle subtended by the semi-diameter 
of the earth's orbit, at the nearest fixed star is insensible. 
The errors to which instrumental measurements are sub- 
ject, arising from the defects of the instruments them- 
selves, from refraction, and from various other sources of 
inaccuracy, are such, that the angular determinations of 
arcs of the heavens cannot be relied on to less than V\ 
But the change of place in any star when viewed at op- 
posite extremities of the earth's orbit, is less than V^, and 
therefore cannot be appreciated by direct measurement. 
It follows, that, when viewed from the nearest star, the 
diameter of the earth's orbit would be insensible. 

322. Taking, however, the annual parallax of a fixed 
star at V^, it can be demonstrated that the distance of 
the nearest fixed star must exceed 95000000 x 200000 = 
190000000x100000, or one hundred thousand times 



321. What do we know respecting the distances of the fixed 
stars ? Hav^e the fixed stars any parallax ? What is taken as 
the base line for measuring the parallax ? W^hat angle is 
greater than would be subtended by the diameter of the earth's 
orbit as seen from the nearest fixed star ? 



262 FIXED STARS. 

one hundred and ninety millions of miles. Of a dis- 
tance so vast we can form no adequate conceptions, and 
even seek to measure it only by the time that light, 
(which moves more than 192,000 miles per second, and 
passes from the sun to the earth in 8m. 13.3sec.,) w^ould 
take to traverse it, which is found to be more than three 
and a half years. 

If these conclusions are drawn with respect to the 
largest of the fixed stars, which we suppose to be vastly 
nearer to us than those of the smallest magnitude, the 
idea of distance swells upon us when we attempt to es- 
timate the remoteness of the latter. As it is uncertain, 
however, whether the difference in the apparent magni- 
tudes of the stars is owing to a real difference, or merely 
to their being at various distances from the eye, more or 
less uncertainty must attend all efforts to determine the 
relative distances of the stars ; but astronomers generally 
believe, that the lower orders of stars are vastly more 
distant from us than the higher. Of some stars it is 
said, that thousands of years would be required for their 
light to travel down to us. 

323. We have said that the stars have no annual par- 
allax ; yet it may be observed that astronomers are not 
exactly agreed on this point. Dr. Brinkley, a late emi- 
nent Irish astronomer, supposed that he had detected an 
annual parallax in Alpha Lyrae amounting to rM3 and 
in Alpha Aquilae of V'A2. These results were contro- 
verted by Mr. Pond, of the Royal Observatory of Green- 
wich ; and Mr. Struve of Dorpat, has shown that in a 
number of cases, the parallax is in a direction opposite 
to that which would arise from the motion of the earth. 
Hence it is considered doubtful whether in all cases of 



322. If we take the parallax at 1", what must the distance 
be ? What time would it take light to traverse this space ? 
How much farther off than this may some of the smaller stars be? 

323. Is it entirely settled that \he fixed stars have no paral- 
lax ? What did Dr. Brinkley assert ? Have his observations 
been confirmed ? 



DISTANCE OF THE FIXED STARS. 263 

an apparent parallax, the effect is not wholly due to 
errors of observation. 

324. Indirect methods have been proposed for ascer- 
taining the parallax of the fixed stars by means of obser- 
vations on the double stars. If the two stars composing 
a double star are at different distances from us, parallax 
would affect them unequally, and change their relative 
positions with respect to each other ; and since the ordi- 
nary som'ces of error arising from the imperfection of 
instruments, from precession, and refraction, would be 
avoided, (since they would affect both objects alike, and 
therefore would not disturb their relative positions,) 
measurements taken with the micrometer of changes 
much less than V^ may be relied on. Sir John Herschel 
proposes a method by which changes may be determined 
which amount to only -^-^ of a second.* 

The immense distance of the fixed stars is inferred 
also from the fact, that the largest telescopes do not in- 
crease their apparent magnitude. They are still points, 
w^hen viewed with the highest magnifiers, although 
they sometimes present a spurious disk, which is owing 
to irradiation, f 



324. What indirect methods have been proposed for ascer- 
taining the parallax of the fixed stars 1 State the particulars 
of this method. Hoav minute changes of place is it supposed 
may be detected. How do the largest telescopes affect their 
apparent magnitudes ? 



* Very recent intelligence informs us, that Prof. Bessel of Konigs- 
berg, has obtained decisive evidence of an annual parallax in 61 Cygni, 
amounting to 0" .3136. This makes the distance of that star, equal to 
657700 times 95 millions of miles — a distance which it would take light 
10.3 years to traverse. 

t Irradiation is an enlargement of objects beyond their proper bounds, 
in consequence of the vivid impression of light on the eye. It is sup- 
posed to increase the apparent diameters of the sun and moon from three 
to four seconds, and to create an appearance of a disk in a fixed star, 
which, when this cause is removed, is seen as a mere point. 



264 FIXED STARS. 



NATURE OF THE STARS. 



325. The stars are bodies greater than our earth. If 
this were not the case they could not be visible at such 
an immense distance. Dr. Wollaston, a distinguished 
English philosopher, attempted to estimate the magni- 
tudes of certain of the fixed stars from the light which 
they afford. By means of an accurate photometer (an 
instrument for measuring the relative intensities of light) 
he compared the hght of Sirius with that of the sun. 
He next inquired how far the sun must be removed from 
us in order to appear no brighter than Sirius. He found 
the distance to be 141,400 times its present distance. 
But Sirius is more than 200,000 times as far off as the 
sun. Hence he inferred that, upon the lowest compu- 
tation, Sirius must actually give out twice as much 
light as the sun ; or that, in point of splendor, Sirius 
must be at least equal to two suns. Indeed, he has ren- 
dered it probable that the light of Sirius is equal to 
fourteen suns. 

326. The fixed stars are suns. We have already seen 
that they are large bodies ; that they are immensely 
farther off than the farthest planet ; that they shine by 
their own light ; in short, that their appearance is, in all 
respects, the same as the sun would exhibit if removed 
to the region of the stars. Hence we infer, that they 
are bodies of the same kind with the sun. 

We are justified therefore by a sound analogy, in con- 
cluding that the stars were made for the same end as 
the sun, namely, as the centers of attraction to other 
planetary worlds, to which they severally dispense light 
and heat. Although the starry heavens present, in a 
clear night, a spectacle of ineffable grandeur and beauty, 



325. Nature of the stars. How large are the stars compared 
with the earth ? How did Dr. Wollaston endeavor to estimate 
the magnitudes of certain fixed stars ? How distant would this 
method make Sirius ? T > how many suns is Sirius equal ? 



SYSTEM OP THE WORLD. 265 

yet it must be admitted that the chief purpose of the 
stars could not have been to adorn the night, since by 
far the greatest part of them are wholly invisible to the 
naked eye ; nor as landmarks to the navigator, for only a 
very small proportion of them are adapted to this pur- 
pose ; nor, finally, to influence the earth by their attrac- 
tions, since their distance renders such an effect entirely 
insensible. If they are suns, and if they exert no im- 
portant agencies upon our vrorld, but are bodies evidently 
adapted to the same purpose as our sun, then it is as ra- 
tional to suppose that they were made to give light and 
heat, as that the eye was made for seeing and the ear 
for hearing. It is obvious to inquire next, to what they 
dispense these gifts if not to planetary worlds ; and why 
to planetary worlds, if not for the use of peixipient be- 
ings ? We are thus led, almost inevitably, to the idea 
of a Plurality of Worlds ; and the conclusion is forced 
upon us, that the spot which the Creator has assigned to 
us is but a humble province of his boundless empire.* 



CHAPTER IV. 

OF THE SYSTEM OF THE WORLD. 

327. The arrangement of all the bodies that compose 
the material universe, and their relations to each other, 
coiutitute the System of the World. 

It is otherwise called the Mechanism of the Heavens ; 
and indeed, in the System of the World, we figure to 
ourselves a machine, all the parts of which have a mu- 



326. Prove that the fixed stars are suns. For what purpose 
were they made ? Could they have been designed to adorn the 
night ? or as landmarks to the navigator ? If they are suns, for 
what farther purpose were they designed ? 

* See this argunxent, in its full extent, in Dick's Celestial Sc€t.ery. 



266 SYSTEM OF THE WORLD. 

tual dependence, and conspire to one great end. " The 
machines that are first invented (says Adam Smith) to 
perform any particular movement, are always the most 
complex ; and succeeding artists generally discover that 
with fewer wheels and with fewer principles of motion 
than had originally been employed, the same effects may 
be more easily produced. The first systems, in the 
same manner, are always the most complex ; and a par- 
ticular connecting chain or principle is generally thought 
necessary to unite every two seemingly disjointed ap- 
pearances ; but it often happens, that one great connect- 
ing principle is afterwards found to be sufficient, to bind 
together all the discordant phenomena that occur in a 
whole species of things." This remark is strikingly 
applicable to the origin and progress of systems of as- 
tronomy. 

328. From the visionary notions which are generally 
understood to have been entertained on this subject by 
the ancients, we are apt to imagine that they knew less 
than they actually did of the truths of astronomy. But 
Pythagoras, who lived 500 years before the Christian 
era, was acquainted with many important facts in our 
science, and entertained many opinions respecting the 
system of the world which are now held to be true. 
Among other things w^ell known to Pythagoras were the 
following : 

1. The principal Constellations. These had begun to 
be formed in the earliest ages of the world. Several of 
them bearing the same names as at present, are men- 
tioned in the writings of Hesiod and Homer ; and the 
" sweet influences of the Pleiades" and the " bands of 
Orion," are beautifully alluded to in the book of Job. 

2. Eclipses. Pythagoras knew both the causes of 
eclipses and how to predict them ; not indeed in the ac- 



l 



327. What constitutes the System of the World ? Under 
what image do we figure it to ourselves ? What properties 
characterize the machines first invented ? 



ASTRONOMICAL KNOWLEDGE OF THE ANCIENTS. 267 

curate manner now employed, but by means of the Saros. 
(Art. 168.) 

3. Pythagoras had divined the true system of the 
world, holding that the sun and not the earth, (as was 
generally held by the ancients, even for many ages after 
Pythagoras,) is the center around which all the planets 
revolve, and that the stars are so many suns, each the 
center of a system like our own. Among lesser things, 
he knew that the earth is round ; that its surface is nat- 
urally divided into five Zones ; and that the ecliptic is 
inclined to the equator. He also held that the earth re- 
volves daily on its axis, and yearly around the sun ; that 
the galaxy is an assemblage of small stars ; and that it 
is the same luminary, namely, Venus, that constitutes 
both the morning and the evening star, whereas, all the 
ancients before him had supposed that each was a sepa- 
rate planet, and accordingly the morning star was called 
Lucifer, and the evening star Hesperus. He held also 
that the planets were inhabited, and even went so far as 
to calculate the size of some of the animals in the moon. 
Pythagoras was so great an enthusiast in music, that he 
not only assigned to it a conspicuous place in his system 
of education, but even supposed the heavenly bodies 
themselves to be arranged at distances corresponding to 
the diatonic scale, and imagined them to pursue their sub- 
lime march to notes created by their own harmonious 
movements, called the " music of the spheres ;" but he 
maintained that this celestial concert, though loud and 
grand, is not audible to the feeble organs of man, but 
only to the gods. 

329. With few exceptions, however, the opinions of 
Pythagoras on the System of the World, were founded 



328. What is said of our usual estimate of the knowledge of 
astronomy possessed by the ancients ? What things were 
known to Pythagoras ? How early were the principal constel- 
lations known ? What did Pythagoras know of eclipses ? Also 
respecting the System of the World ? What lesser things did 
he know ? What notions had he of the music of the spheres ? 



268 SYSTEM OF THE WORLD. 

in tnith. Yet they were rejected by Aristotle and by 
most succeeding astronomers down to the time of Coper- 
nicus, and in their place was substituted the doctrine of 
Crystalline Spheres, first taught by Eudoxus. Accord- 
ing to this system, the heavenly bodies are set like gems 
in hollow solid orbs, composed of crystal so pellucid that 
no anterior orb obstructs in the least the view of any of 
the orbs that lie behind it. The sun and the planets 
have each its separate orb ; but the fixed stars are all set 
in the same grand orb ; and beyond this is another still, 
the Primum Mobile, which revolves daily from east to 
west, and carries along with it all the other orbs. Above 
the whole, spreads the Grand Empyrean, or third heav- 
ens, the abode of perpetual serenity. 

To account for the planetary motions, it was supposed 
that each of the planetary orbs as well as that of the sun, 
has a motion of its own eastward, while it partakes of 
the common diurnal motion of the starry sphere. Aris- 
totle taught that these motions are effected by a tutelaiy 
genius of each planet, residing in it, and directing its 
motions, as the mind of man directs his motions. 

330. On coming down to the time of Hipparchus, who 
flourished about 150 years before the Christian era, we 
meet with astronomers who acquired far more accurate 
knowledge of the celestial motions. Previous to this 
period, celestial observations were made chiefly with the 
naked eye, but Hipparchus w^as in possession of instru- 
ments for measuring angles, and knew how to resolve 
spherical triangles. He ascertained the length of the 
year within 6m. of the truth. He discovered the eccen- 
tricity of the solar orbit, (although he supposed the sun 
actually to move uniformly in a circle, but the earth to 
be placed out of the center,) and the positions of the 



329. "Were the opinions of Pythagoras generally embraced 
by the ancients? What was the doctrine of Crystalline 
Spheres ? How were the planetary motions accounted for ? 

330. When did Hipparchus flourish 1 How did he make 
his observations ? What great facts did he ascertain ? 



THE PTOLEMAIC SYSTEM. 269 

sun's apogee and perigee. He formed very accurate es- 
timates of the obliquity of the ecliptic, and of the preces- 
sion of the equinoxes. He computed the exact period 
of the synodic revolution of the moon, and the inclina- 
tion of the lunar orbit ; discovered the motion of her 
node and of her Hne of apsides ; and made the first at- 
tempts to ascertain the horizontal parallaxes of the sun 
and moon. 

Such was the state of astronomical knovrledge vrhen 
Ptolemy wrote the Almagest, in which he has transmit- 
ted to us an encyclopaedia of the astronomy of the an- 
cients. 

331. The systems of the world which have been most 
celebrated are three — the Ptolemaic, the Tychonic, and 
the Copernican. We shall conclude this part of our 
work with a concise statement and discussion of each 
of these systems of the Mechanism of the Heavens. 

THE PTOLEMAIC SYSTEM. 

332. The doctrines of the Ptolemaic System were not 
originated by Ptolemy, but being digested by him out of 
materials furnished by various hands, it has come down 
to us under the sanction of his name. 

According to this system, the earth is the center of 
the miiverse, and all the heavenly bodies daily revolve 
around it from east to west. In order to explain the 
planetary motions, Ptolemy had recourse to deferents and 
epicycles — an explanation devised by Apollonius one of 
the greatest geometers of antiquity. He conceived that, 
in the circumference of a circle, having the earth for its 
center, there moves the center of another circle, in the 
circumference of which the planet actually revolves. 
The circle surrounding the eai'th was called the deferent. 



331. What are the most celebrated Systems of the World? 

332. Ptolemaic System. — Did Ptolemy originate this sys- 
tem? State the outlines of it. What was the deferent? 
What was the epicycle " 



23* 



270 



SYSTEM OF THE WOELD. 



while the smaller circle whose center was always in the 
periphery of the deferent, was called the epicycle. The 
motion in each was supposed to be uniform. La'stly, it 
was conceived that the motion of the center of the epi- 
cycle in the circumference of the deferent, and of the 
planet in that of the epicycle, are in the same directions. 

333. But these views will be better understood from a 
diagram. Therefore, let ABC (Fig. 53,) represent the 
deferent, E being the earth a little out of the center. 

Fig. 53. 




Let abc represent the epicycle, having its center at v, on 
the periphery of the deferent. Conceive the circumfer- 
ence of the deferent to be carried about the earth every 
twenty four hours in the order of the letters ; and at the 



333. Explain the Ptolemaic System by figure 53. 



THE PTOLEMAIC SYSTEM. 271 

same time, let the center v of the epicycle abed, have a 
slow motion in the opposite direction, and let a body re- 
volve in this circle in the direction abed. Then a body 
revolving in the circle abed, and at the same time having 
a motion eastw^ard in common with the circle, would 
describe the looped curves klmnop. At I and m, and at 
n and o, it would appear stationary, because in these 
points its motion would be either directly towards or 
from the spectator. The motion would be direct from 
k to I, being in the order of the signs, and retrograde 
from I to m ; direct again from m to n, and retrograde 
from n to o, 

334. Such a deferent and epicycle may be devised 
for each planet as will fully explain all its ordinaiy mo- 
tions ; but it is inconsistent with the phases of Mercury 
and Venus, which being between us and the sun on 
both sides of the epicycle, would present their dark 
sides towards us in both these positions, whereas at one 
of the conjunctions they are seen to shine with full 
face. It is moreover absurd to speak of a geometrical 
center which has no bodily existence, moving around the 
earth on the circumference of another circle ; and hence 
some suppose that the ancients merely assumed this hy- 
pothesis as affording a convenient geometrical represen- 
tation of the Phenomena, — a diagram simply, without 
conceiving the system to have any real existence in na- 
ture. 

335. The objeetions to the Ptolemaic system, in gen- 
eral, are the following : Fb'st, it is a mere hypothesis, 
having no evidence in its favor, except that it explains 
the phenomena. This evidence is insufficient of itself, 
since it frequently happens that each of two hypotheses, 



334. State the objections to this mode of representing the 
motions of the planets. Why is it inconsistent with the phases 
of Mercury and Venus 1 What is said of the supposition of a 
geometrical center moving around the earth ? 



272 SYSTEM OF THE WORLD. 

directly opposite to each other, will explain all the known 
phenomena. But the Ptolemaic system does not even 
do this, as it is inconsistent with the phases of Mercury 
and Venus, as already observed. Secondly, now that 
we are acquainted with the distances of the remoter 
planets, and especially of the fixed stars, the swiftness 
of motion implied in a daily revolution of the starry 
firmament around the earth, renders such a motion 
wholly incredible. Thirdly, the centrifugal force that 
would be generated in these bodies, especially in the 
sun, renders it impossible that they can continue to re- 
volve around the earth as a center. 

These reasons are sufficient to show the absurdities 
of the Ptolemaic System of the World. 

THE TYCHOXIC SYSTEM. 

336. Tycho Brahe, like Ptolemy, placed the earth in 
the center of the universe, and accounted for the diur- 
nal motions in the same manner as Ptolemy had done, 
namely, by an actual revolution of the whole host of 
heaven around the earth every twenty four hours. But 
he rejected the scheme of deferents and epicycles, and 
held that the moon revolves about the earth as the cen- 
ter of her motions ; that the sun and not the earth, is 
the center of the planetary motions ; and that the sun 
accompanied by the planets moves around the earth 
once a year, somewhat in the manner that we now con- 
ceive of Jupiter and his satellites as revolving around 
the sun. 

337. The system of Tycho serves to explain all the 
common phenomena of the planetary motions, but it is 
encumbered with the same objections as those that have 



335. Slate the objections to the Ptolemaic System in general. 
Does it explain all the phenomena ? What swiftness of motion 
does it imply ? 

336. Tychonic System. — State its leading points. 



THE COPERNICAIf SYSTEM. 273 

been mentioned as resting against the Ptolemaic system, 
namely, that it is a mere hypothesis ; that it implies an 
incredible swiftness in the diurnal motions ; and that it 
IS inconsistent with the known laws of universal grav- 
itation. But if the heavens do not revolve, the earth 
must, and this brings us to the system of Copernicus. 

THE COPERNICAN SYSTEM. 

338. Copernicus was born at Thorn in Prussia in 
1473. The system that bears his name was the fruit of 
forty years of intense study and meditation upon the 
celestial motions. As already mentioned, (Art. 6,) it 
maintains (1) That the apparent diurnal motions of the 
heavenly bodies, from east to west is owing to the real 
revolution of the earth on its own axis from west to east ; 
and (2) That the sun is the center around which the 
earth and planets all revolve from west to east. It rests 
on the following arguments : 

First, the earth revolves on its own axis. 

1. Because this supposition is vastly more simple. 

2. It is agreeable to analogy, since all the other plan- 
ets that afford any means of determining the question, 
are seen to revolve on their axes. 

3. The spheriodal figure of the earth, is the figure of 
equiHbrium, that results from a revolution on its axis. 

4. The diminished weight of bodies at the equator, 
indicates a centrifugal force arising from such a rev- 
olution. 

5. Bodies let fall from a high eminence, fall eastward 
of their base, indicating that when farther from the cen- 
ter of the earth they were subject to a greater velocity, 
which in consequence of their inertia, they do not en- 
tirely lose in descending to the lower level. 



337. How far does the Tychonic System explain the plan- 
etary motions ? With what objections is it encumbered ? 

338. Copernican System. — Who was Copernicus? State 
the principles of his System. State the five reasons why the 
earth revolves on its axis. 



274 SYSTEM OF THE WORLD. 

339. Secondly, the planets, including the earth, revelve 
about the sun. 

1. The phases of Mercury and Venus are precisely 
such, as would result from their circulating around the 
sun in orbits within that of the earth; but they are 
never seen in opposition, as they would be if they cir- 
culate around the earth. 

2. The superior planets do indeed revolve around the 
earth ; but they also revolve around the sun, as is evi- 
dent from their phases and from the known dimensions 
of their orbits ; and that the sun and not the earth, is the 
center of their motions, is inferred from the greater sym- 
metry of their motions as referred to the sun than as re- 
ferred to the earth, and especially from the laws of grav- 
itation which forbid our supposing that bodies so much 
larger than the earth, as some of these bodies are, can 
circulate permanently around the earth, the latter re- 
maining all the while at rest. 

3. The annual motion of the earth itself is indicated 
also by the most conclusive arguments. For, first, since 
all the planets with their satellites, and the comets, re- 
volve about the sun, analogy leads us to infer the same 
respecting the earth and its satellites. Secondly, The 
motions of the satellites, as those of Jupiter and Saturn, 
indicate that it is a law of the solar system that the 
smaller bodies revolve about the larger. Thirdly, on 
the supposition that the earth performs an annual revolu 
tion around the sun, it is embraced along with the plan- 
ets, in Kepler's law, that the squares of the times are as 
the cubes of the distances ; otherwise, it forms an ex- 
ception, and the only known exception to this law. 

340. It only remains to inquire, whether there sub- 
sist higher orders of relations between the stars them- 
selves. 



339. State the three reasons why the planets revolve about 
the sun — how argued from the phases of Mercury and Venus ? 
from the aspects and positions of the superior planets 1 from 
the annual motion of the earth ? 



THE COPER]VICAN SYSTEM. 275 

The revolutions of the binary stars afford conclusive 
evidence of at least subordinate systems of suns, gov- 
erned by the same laws as those w^hich regulate the mo- 
tions of the solar system. The nehidcB also compose 
peculiar systems, in which the members are evidently 
bound together by some common relation. 

In these marks of organization, — of stars associated 
together in clusters, — of sun revolving around sun, — 
and of nebulae disposed in regular figures, we recognize 
different members of some grand system, links in one 
great chain that binds together all parts of the universe ; 
as we see Jupiter and his satellites combined in one sub- 
ordinate system, and Saturn and his satellites in another, 
— each a vast kingdom, and both uniting with a num- 
ber of other individual parts to compose an empire still 
more vast. 

341. This fact being now estabhshed, that the stars 
are immense bodies like the sun, and that they are sub- 
ject to the laws of gravitation, we cannot conceive how 
they can be preserved from falling into final disorder and 
ruin, unless they move in harmonious concert like the 
members of the solar system. Otherwise, those that 
are situated on the confines of creation, being retained 
by no forces from without, while they are subject to the 
attraction of all the bodies within, must leave their sta- 
tions, and move inward with accelerated velocity, and 
thus all the bodies in the universe would at length fall 
together in the common center of gravity. The im- 
mense distance at which the stars are placed from each 
other, would indeed delay such a catastrophe ; but such 
must be the ultimate tendency of the material world, un- 



340. Proofs of higher orders of relations among the stars 
themselves — from the binary stars — from the nebulae. What 
do we recognize in these marks of organization 1 

341. How are these systems preserved from falling into dis- 
order and ruin ? How should we be justified in inferring that 
other worlds are not subject to forces which operate to hasten 
their decay 1 To what final conclusions are we led 1 



SYSTEM OF THE WORLD. 



less sustained in one harmonious system by nicely ad- 
justed motions. To leave entirely out of view our con- 
fidence in the wisdom and preserving goodness of the 
Creator, and reasoning merely from what we know of 
the stability of the solar system, we should be justified 
in inferring, that other worlds are not subject to forces 
which operate only to hasten their decay, and to involve 
them in final ruin. 

We conclude, therefore, that the material universe is 
one great system ; that the combination of planets with 
their satellites constitutes the first or lowest order of 
worlds ; that next to these planets are linked to suns ; 
that these are bound to other suns, composing a still 
higher order in the scale of being ; and, finally, that all 
the different systems of worlds, move around their com- 
mon center of gravity. 



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